No description available.

No description available.

No description available.

A topological group is an abstract group which is also a topological space and in which the group operation are continuous. In group theory the algebraic binary operation of passage to a limit is studied in a similar manner. The two fundamental mathematical concepts of binary operation and passage to a limit are united and interrelated in the concept of topological group. The concept of topological groups arose from the study of continuous transformations. However, topological groups can be studied quite independently from continuous transformations and the latter can be presented as applications of topological groups. The first person to consider topological groups was Lie, but he was concerned with groups defined by analytic operations. Later, around 1900-1910 other men, beginning with Hilbert and Brouwer, studied more general topological groups. The topological group is then -- from a logical point of view only -- a combination of the abstract group and the topological space. Hence, the first and second chapters of this paper will be devoted to the concept of abstract group and topological space respectively, while the third and main chapter will utilize these two concepts in the formation and study of the topological group. Our main source of information will be Leon Pontrjagin's book, "Topological Groups" (1939); however, our approach will be somewhat broader and we will include results from other sources and our own investigations. In order to avoid making this paper to lengthy for its purpose, we will prove only some of the theorems. The rest of them will be simply stated and often followed by a sketch or an outline of the proof. The major definitions and theorems and all the examples will be numbered consecutively as they appear. For instance "Theorem 2.5" is the fifth numbered item in the second chapter.

Thesis (M.A.)--York University, 2008. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 166-167). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR45921

No description available.

Revised version of the author's Ph. D. thesis, Free University, Amsterdam. / Includes bibliographical references (p. 236-245) and index.

The notion of a topological group follows naturally from a combination of the properties of a group and a topological space. Since a group consists of a set G of elements which may be either finite or infinite and since this is also common to a topological space, a question is opened as to whether or not it is possible to assign a topology to a set of elements which form a group under a certain operation. Now it is possible to assign a topology to any set of elements if no restriction is placed on the topology assigned and hence this study would be of little value from the standpoint of the group itself. If however it is required that the group operation be continuous in the topological space then a very interesting theory is developed.

No description available.

Let F denote the field of real numbers, complex numbers, or a finite algebraic extension of the p-adic field. We prove that the special linear group SLn(F) with the usual topology induced by F is a minimal topological group. This is accomplished by first proving the minimality of the upper triangular group in SLn(F). The proof for the upper triangular group uses an induction argument on a chain of upper triangular subgroups and relies on general results for locally compact topological groups, quotient groups, and subgroups. Minimality of SLn(F) is concluded by appealing to the associated Lie group decomposition as the product of a compact group and an upper triangular group. We also prove the universal minimality of homeomorphism groups of one dimensional manifolds, and we give a new simple proof of the universal minimality of S∞.