The Interval [0,1] Admits no Functorial Embedding into a Finite-Dimensional or Metrizable Topological Group

An embedding X ⊂ G of a topological space X into a topological group G is called functorial if every homeomorphism of X extends to a continuous group homomorphism of G. It is shown that the interval [0, 1] admits no functorial embedding into a finite-dimensional or metrizable topological group.

Topological Dichotomy and Unconditional Convergence

In this paper, we give a criterion for unconditional convergence with respect to some summability methods, dealing with the topological size of the set of choices of sign providing convergence. We obtain similar results for boundedness. In particular, quasi-sure unconditional convergence implies unconditional convergence.

Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where Ω is the first uncountable ordinal number, then Bα (X) is uncomplemented as a closed subspace of Bβ (X). These assertions for X = [0, 1] were proved by W. G. Bade [4] and in the case when X contains an uncountable compact metrizable space – by F.K.Dashiell [9]. Our argumentation is one non-metrizable modification of both Bade’s and Dashiell’s methods.

Doitchinov's Construct of Supertopological Spaces is Topological

It is shown that the construct of supertopological spaces and continuous maps is topological.

Regular and Other Kinds of Extensions of Topological Spaces

∗ This work was partially supported by the National Foundation for Scientific Researches at the Bulgarian Ministry of Education and Science under contract no. MM-427/94.

Neural Network Based Optimal Control with Constraints

In the present paper the problems of the optimal control of systems when constraints are imposed on the control is considered. The optimality conditions are given in the form of Pontryagin’s maximum principle. The obtained piecewise linear function is approximated by using feedforward neural network. A numerical example is given.

Formalization of Structural Constraints of Relationships in Model „Entity-Relationship”

The basic conceptions of the model „entity-relationship” as entities, relationships, structural constraints of the relationships (index cardinality, participation degree, and structural constraints of kind (min, max)) are considered and formalized in terms of relations theory. For the binary relations two operators (min and max) are introduced; structural constraints are determined in terms of the operators; the main theorem about compatibility of these operators’ values on the source relation and inversion to it is given here.

Automata–based Method for Solving Systems of Linear Constraints in {0,1}

We consider a finite state automata based method of solving a system of linear Diophantine equations with coefficients from the set {-1,0,1} and solutions in {0,1}.

One's own country and familiar places in the mind's eye:different topological representations for navigational and non-navigational contents

Visual mental imagery is a process that draws on different cognitive abilities and is affected by the contents of mental images. Several studies have demonstrated that different brain areas subtend the mental imagery of navigational and non-navigational contents. Here, we set out to determine whether there are distinct representations for navigational and geographical images. Specifically, we used a Spatial Compatibility Task (SCT) to assess the mental representation of a familiar navigational space (the campus), a familiar geographical space (the map of Italy) and familiar objects (the clock). Twenty-one participants judged whether the vertical or the horizontal arrangement of items was correct. We found that distinct representational strategies were preferred to solve different categories on the SCT, namely, the horizontal perspective for the campus and the vertical perspective for the clock and the map of Italy. Furthermore, we found significant effects due to individual differences in the vividness of mental images and in preferences for verbal versus visual strategies, which selectively affect the contents of mental images. Our results suggest that imagining a familiar navigational space is somewhat different from imagining a familiar geographical space. © 2014 Elsevier Ireland Ltd.

Approximating the MaxMin and MinMax Area Triangulations using Angular Constraints

* A preliminary version of this paper was presented at XI Encuentros de Geometr´ia Computacional, Santander, Spain, June 2005.

Explicit Solutions of Nonlocal Boundary Value Problems, Containing Bitsadze-Samarskii Constraints

MSC 2010: 44A35, 35L20, 35J05, 35J25

Optimality Conditions for D.C. Vector Optimization Problems under D.C. Constraints

2000 Mathematics Subject Classification: Primary 90C29; Secondary 49K30.

Pseudo-Compact Semi-Topological Groups

Митрофан М. Чобан, Петър Ст. Кендеров, Уорън Б. Муурс - Полу-топологична група (съответно, топологична група) е група, снабдена с топология, относно която груповата оперция произведение е частично непрекъсната по всяка от променливите (съответно, непрекъсната по съвкупност от променливите и обратната операция е също непрекъсната). В настоящата работа ние даваме условия, от топологичен характер, една полу-топологична група да е всъщност топологична група. Например, ние показваме, че всяка сепарабелна псевдокомпактна полу-топологична група е топологична група. Показваме също, че всяка локално псевдокомпактна полу-топологична група, чиято групова операция е непрекъсната по съвкупност от променливите е топологична група.

About Topological Groups and the Baire Property in Remainders

Александър В. Архангелски, Митрофан М. Чобан, Екатерина П. Михайлова - Изследвани са прирасти със свойството на Бер на топологични групи.

Control Systems with Constraints and Uncertain Initial Conditions

AMS subject classification: 49N55, 93B52, 93C15, 93C10, 26E25.