Some problems in set topology relating group of homeomorphisms and order

In this thesis we investigate some problems in set theoretical topology related to the concepts of the group of homeomorphisms and order. Many problems considered are directly or indirectly related to the concept of the group of homeomorphisms of a topological space onto itself. Order theoretic methods are used extensively. Chapter-l deals with the group of homeomorphisms. This concept has been investigated by several authors for many years from different angles. It was observed that nonhomeomorphic topological spaces can have isomorphic groups of homeomorphisms. Many problems relating the topological properties of a space and the algebraic properties of its group of homeomorphisms were investigated. The group of isomorphisms of several algebraic, geometric, order theoretic and topological structures had also been investigated. A related concept of the semigroup of continuous functions of a topological space also received attention

Studies on the seaweeds of andaman and nicobar group of islands

The importance of marine algae, often referred to as seaweeds, has been felt over a long time and is appreciated more and more in modern times. The economic value of marine algae is understood both indirectly and directly. The indirect benefit is due to the role of marine phytoplankton as well as the benthic macrophyte biomass along the shore and in the continental shelf, in primary production of the sea. Direct benefit includes the use of marine algae as food, feed, fertilizer and as source of various products of commercial importance such as agar and alginic acid. Hence to understand the potential resources of seaweeds, their distribution, density, standing crop and interrelated environmental parameters, a detailed study (survey and ecological work) was carried out for a period of 20 months from August 1988 to March 1990 in South Andaman, North Andaman, Middle Andaman, Havelock, Neil, Car Nicobar, Terassa, Chowra and Bumpoka islands. However in South Andaman, data were collected from five fixed stations fortnightly during this period for the purpose of modelling and system analysis.

Maximal compactness, min- imal Hausdor ness and reversibility of frames and a study on automorphism group of frames

One can do research in pointfree topology in two ways. The rst is the contravariant way where research is done in the category Frm but the ultimate objective is to obtain results in Loc. The other way is the covariant way to carry out research in the category Loc itself directly. According to Johnstone [23], \frame theory is lattice theory applied to topology whereas locale theory is topology itself". The most part of this thesis is written according to the rst view. In this thesis, we make an attempt to study about 1. the frame counterparts of maximal compactness, minimal Hausdor - ness and reversibility, 2. the automorphism groups of a nite frame and its relation with the subgroups of the permutation group on the generator set of the frame