This paper will be devoted to an exposition of some of the basic properties of paracompact spaces. In particular, it will be shown that every pseudo-metrizable space is paracompact and countably paracompact.

The purpose of this thesis is to investigate the idea of topological "connectedness" by presenting some of the basic ideas concerning connectedness along with several related concepts.

The study of metric spaces is closely related to the study of topology in that the study of metric spaces concerns itself, also, with sets of points and with a limit point concept based on a function which gives a "distance" between two points. In some topological spaces it is possible to define a distance function between points in such a way that a limit point of a set in the topological sense is also a limit point of the same set in a metric sense. In such a case the topological space is "metrizable". The real numbers with its usual topology is an example of a topological space which is metrizable, the distance function being the absolute value of the difference of two real numbers. Chapters II and III of this thesis attempt to classify, to a certain extent, what type of topological space is metrizable. Chapters IV and V deal with several properties of metric spaces and certain functions of metric spaces, respectively.

Cheng Hon-wing. / Thesis (M.Phil.)--Chinese University of Hong Kong. / Bibliography: leaf 29.

Thesis (Ph.D.)--York University, 2004. Graduate Programme in Mathematics. / Typescript. Includes bibliographical references (leaves 77-83) and index. Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ99185

<p>The main purpose of this thesis is to study the interplay between relational structures and topology , and to portray pairings in terms of some finite poset models and order preserving maps. We show the interrelations between the categories of topological spaces, closure spaces and relational structures. We study the 4-point non-Hausdorff model S4 weakly homotopy equivalent to the circle S1. We study pairings of some objects in the category of relational structures similar to the multiplication S4 x S4- S4 S4 fails to be order preserving for posets. Nevertheless, applying a single barycentric subdivision on S4 to get S8, an 8-point model of the circle enables us to define an order preserving poset map S8 x S8- S4. Restricted to the axes, this map yields weak homotopy equivalences S8 x S8, we obtain a version of the Hopf map S8 x S8s - SS4. This model of the Hopf map is in fact a map of non-Hausdorff double map cylinders.</p>

Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1931. / Vita. "Sonderabdruck aus der "Mathematischen zeitschrift", Band 33, Heft 5"--T.p. verso. Includes bibliographical references.

Thesis--Université de Paris XI. / Includes bibliographical references.

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In this treatise the convergence of iterative algorithms for the solution of non-linear operator equations in complex linear topological spaces are studied from the point of view of fixed-point theorems in such spaces... It was felt that the concept of the Gâteaux differential is a more natural one to use in connection with linear topological spaces. The beauty of the developed technique we mentioned earlier is essentially due to the fact that we are considering spaces over the complex number field. The resulting convergence theorems have also the added advantage of imposing no conditions on the second or higher order differentials of the operator T, as would be the case in an obvious extension ( which was not written down) of Kantorovich's work to such real linear topological spaces. [...]