Some properties of g- and P-spaces

A γ-space with a strictly positive measure is separable. An example of a non-separable γ−space with c.c.c. is given. A P−space with c.c.c. is countable and discrete.

Paracompact Spaces and Radon Spaces

We prove that if E is a subset of a Banach space whose density is of measure zero and such that (E, weak) is a paracompact space, then (E, weak) is a Radon space of type (F ) under very general conditions.

Continuity of Pseudo-differential Operators on Bessel And Besov Spaces

We study the continuity of pseudo-differential operators on Bessel potential spaces Hs|p (Rn ), and on the corresponding Besov spaces B^(s,q)p (R ^n). The modulus of continuity ω we use is assumed to satisfy j≥0, ∑ [ω(2−j )Ω(2j )]2 < ∞ where Ω is a suitable positive function.

Hausdorff Measures of Noncompactness and Interpolation Spaces

2000 Mathematics Subject Classification: 46B50, 46B70, 46G12.

Blurring the lines between public and private spaces in residential design

This thesis explores the role of public space as an integral part of residential design to promote a sense of community, where neighbors can congregate and children can play in safety. ^ Through research and analysis of successful public spaces, I evaluated relationships between dwellings and public spaces that offer progressive levels of privacy, and between indoor and outdoor spaces. Further research of published studies on child development, human behavior and relationships with nature identified a human preference for natural environments, a need for adequate recreation space for children's development and the potential of open spaces to build a strong sense of community. ^ My project develops multiple transitional spaces between the street and the interior of dwellings that provide varying degrees of privacy closely related to the community's green spaces. The result is a community-oriented pedestrian environment that encourages family and community values and contributes to the healthy living of its residents without depriving them of their privacy. ^

What happens at the gap between knowledge and practice? Spaces of encounter and misencounter between environmental scientists and local people

Researchers studying processes of global environmental change are increasingly interested in their work having impacts that go beyond academia to influence policy and management. Recent scholarship in the conservation sciences has pointed to the existence of a research-action gap and has proposed various solutions for overcoming it. However, most of these studies have been limited to the spaces of dissemination, where the science has already been done and is then to be passed over to users of the information. Much less attention has been paid to encounters that occur between scientists and nonscientists during the practice of doing scientific research, especially in situations that include everyday roles of labor and styles of communication (i.e., fieldwork). This paper builds on theories of contact that have examined encounters and relations between different groups and cultures in diverse settings. I use quantitative and qualitative evidence from Madidi National Park, Bolivia, including an analysis of past research in the protected area, as well as interviews (N = 137) and workshops and focus groups (N = 12) with local inhabitants, scientists, and park guards. The study demonstrates the significance of currently unacknowledged or undervalued components of the research-action gap, such as power, respect, and recognition, to develop a relational and reciprocal notion of impact. I explain why, within such spaces of encounter or misencounter between scientists and local people, knowledge can be exchanged or hidden away, worldviews can be expanded or further entrenched, and scientific research can be welcomed or rejected.

Participation Space Studies: a socio-technical exploration of activist and community groups’ use of online and offline spaces to support their work

Participation Space Studies explore eParticipation in the day-to-day activities of local, citizen-led groups, working to improve their communities. The focus is the relationship between activities and contexts. The concept of a participation space is introduced in order to reify online and offline contexts where people participate in democracy. Participation spaces include websites, blogs, email, social media presences, paper media, and physical spaces. They are understood as sociotechnical systems: assemblages of heterogeneous elements, with relevant histories and trajectories of development and use. This approach enables the parallel study of diverse spaces, on and offline. Participation spaces are investigated within three case studies, centred on interviews and participant observation. Each case concerns a community or activist group, in Scotland. The participation spaces are then modelled using a Socio-Technical Interaction Network (STIN) framework (Kling, McKim and King, 2003). The participation space concept effectively supports the parallel investigation of the diverse social and technical contexts of grassroots democracy and the relationship between the case-study groups and the technologies they use to support their work. Participants’ democratic participation is supported by online technologies, especially email, and they create online communities and networks around their goals. The studies illustrate the mutual shaping relationship between technology and democracy. Participants’ choice of technologies can be understood in spatial terms: boundaries, inhabitants, access, ownership, and cost. Participation spaces and infrastructures are used together and shared with other groups. Non-public online spaces, such as Facebook groups, are vital contexts for eParticipation; further, the majority of participants’ work is non-public, on and offline. It is informational, potentially invisible, work that supports public outputs. The groups involve people and influence events through emotional and symbolic impact, as well as rational argument. Images are powerful vehicles for this and digital images become an increasingly evident and important feature of participation spaces throughout the consecutively conducted case studies. Collaboration of diverse people via social media indicates that these spaces could be understood as boundary objects (Star and Griesemer, 1989). The Participation Space Studies draw from and contribute to eParticipation, social informatics, mediation, social shaping studies, and ethnographic studies of Internet use.

DOCUMENT CONTROL OF NATIONAL MAPPING AND METRIC STUDIES CHARACTERIZING NATIONAL IDENTITY AND INDIVIDUAL. I STAGE

This is a project of the School of Library, Documentation and Information of the National University, is performed to support the initiative of UNESCO to build the Memory of the World (UNESCO, 1995) and to help provide universal access to documentation. To this end, the School of Library Science students has promoted the realization of final graduation work on documentary control of domestic production. This project has the following objectives:Objectives1. Conduct mapping national documentary through the identification, analysis, organization and access to documentary heritage of Costa Rica, to contribute to the Memory of the World.2. Perform bibliometric analysis of documentary records contained in the integrated databases.This project seeks to bring undergraduate students graduating from the school, in making final graduation work on document control. Students have the opportunity to make final graduation work on the documentary production of Costa Rica on a specific theme or on a country's geographical area.Desk audits aimed at identifying the document using access points and indicate its contents to allow recovery by the user.The result is the production of a new document, other than the original, a secondary document: the bibliography. The records in the database each control documentation completed work will be integrated into a single database to be placed on the website of EBDI, for consultation of researchers and interested users.

Navigating, recognizing and describing urban spaces with vision and lasers

In this paper we describe a body of work aimed at extending the reach of mobile navigation and mapping. We describe how running topological and metric mapping and pose estimation processes concurrently, using vision and laser ranging, has produced a full six-degree-of-freedom outdoor navigation system. It is capable of producing intricate three-dimensional maps over many kilometers and in real time. We consider issues concerning the intrinsic quality of the built maps and describe our progress towards adding semantic labels to maps via scene de-construction and labeling. We show how our choices of representation, inference methods and use of both topological and metric techniques naturally allow us to fuse maps built from multiple sessions with no need for manual frame alignment or data association.

Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

On Chaos and Fractals in General Topological Spaces

The present study on chaos and fractals in general topological spaces. Chaos theory originated with the work of Edward Lorenz. The phenomenon which changes order into disorder is known as chaos. Theory of fractals has its origin with the frame work of Benoit Mandelbrot in 1977. Fractals are irregular objects. In this study different properties of topological entropy in chaos spaces are studied, which also include hyper spaces. Topological entropy is a measures to determine the complexity of the space, and compare different chaos spaces. The concept of fractals can’t be extended to general topological space fast it involves Hausdorff dimensions. The relations between hausdorff dimension and packing dimension. Regular sets in Metric spaces using packing measures, regular sets were defined in IR” using Hausdorff measures. In this study some properties of self similar sets and partial self similar sets. We can associate a directed graph to each partial selfsimilar set. Dimension properties of partial self similar sets are studied using this graph. Introduce superself similar sets as a generalization of self similar sets and also prove that chaotic self similar self are dense in hyper space. The study concludes some relationships between different kinds of dimension and fractals. By defining regular sets through packing dimension in the same way as regular sets defined by K. Falconer through Hausdorff dimension, and different properties of regular sets also.

GEOMETRIC RELATIONS BETWEEN SPACES OF NUCLEAR OPERATORS AND SPACES OF COMPACT OPERATORS

We extend and provide a vector-valued version of some results of C. Samuel about the geometric relations between the spaces of nuclear operators N(E, F) and spaces of compact operators K(E, F), where E and F are Banach spaces C(K) of all continuous functions defined on the countable compact metric spaces K equipped with the supremum norm. First we continue Samuel's work by proving that N(C(K-1), C(K-2)) contains no subspace isomorphic to K(C(K-3), C(K-4)) whenever K-1, K-2, K-3 and K-4 are arbitrary infinite countable compact metric spaces. Then we show that it is relatively consistent with ZFC that the above result and the main results of Samuel can be extended to C(K-1, X), C(K-2,Y), C(K-3, X) and C(K-4, Y) spaces, where K-1, K-2, K-3 and K-4 are arbitrary infinite totally ordered compact spaces; X comprises certain Banach spaces such that X* are isomorphic to subspaces of l(1); and Y comprises arbitrary subspaces of l(p), with 1 < p < infinity. Our results cover the cases of some non-classical Banach spaces X constructed by Alspach, by Alspach and Benyamini, by Benyamini and Lindenstrauss, by Bourgain and Delbaen and also by Argyros and Haydon.

On paracompactness, completeness and boundedness in uniform spaces

Recently two new types of completeness in metric spaces, called Bourbaki-completeness and cofinal Bourbaki-completeness, have been introduced in [7]. The purpose of this note is to analyze these completeness properties in the general context of uniform spaces. More precisely, we are interested in how they are related with uniform paracompactness properties, as well as with some kind of uniform boundedness.

From bricks to clicks : hybrid commercial spaces in the landscape of early literacy and learning

In their quest for resources to support children’s early literacy learning and development, parents encounter and traverse different spaces in which discourses and artifacts are produced and circulated. This paper uses conceptual tools from the field of geosemiotics to examine some commercial spaces designed for parents and children which foreground preschool learning and development. Drawing on data generated in a wider study I discuss some of the ways in which the material and virtual commercial spaces of a transnational shopping mall company and an educational toy company operate as sites of encounter between discourses and artifacts about children’s early learning and parents of preschoolers. I consider how companies connect with and ‘situate’ people as parents and customers, and then offer pathways designed for parents to follow as they attempt to meet their very young children’s learning and development needs. I argue that these pathways are both material and ideological, and that are increasingly tending to lead parents to the online commercial spaces of the world wide web. I show how companies are using the online environment and hybrid offline and online spaces and flows to reinforce an image of themselves as authoritative brokers of childhood resources for parents that is highly valuable in a policy climate which foregrounds lifelong learning and school readiness.