Overview
ABSTRACT
General topology is the branch of mathematics that deals with the fundamental concepts used in topology, and their properties. Theoretical and applicational utility is found in all branches of analysis and geometry, and in many other scientific disciplines outside mathematics. This article concerns topological spaces, and covers the basics of these spaces, which are sets in which neighborhoods are rigorously defined in all of their points, convergent sequences of points and subsets, and continuous applications between two such spaces. The major concepts are those of separation, countability, compactness and connectedness.
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Jean-Charles PINOLI : Professor - École Nationale Supérieure des Mines de Saint-Étienne, Saint-Étienne, France - To Andrée-Aimée Toucas for her bibliographical support. - To Professor Johan Debayle for his scientific interest.
INTRODUCTION
General topology is presented in a series of six articles: the first two [AF97]
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KEYWORDS
continuity | compactness | connectedness | convergence
Topological Spaces I. Basic Notions
Preamble
Bibliography
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