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ABSTRACT
General topology is the branch of mathematics that deals with the fundamental concepts used in topology, and their properties. Its theoretical and applicational utility is found in all branches of analysis and geometry, and in many other scientific disciplines outside mathematics. This article covers the basics of metric space, i.e. sets in which distances between points are rigorously defined, and which are very useful topological spaces. Then come the major topological concepts of separation, countability, compactness and connectedness in metric spaces, and the concept of boundedness. Lastly, metrizability and the fixed-point theorems are addressed.
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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 Yann Gavet for his scientific interest.
INTRODUCTION
General topology is presented in a series of six articles; the first two
Reading the two articles in the series on topological spaces
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KEYWORDS
compactness | connectedness | fixed-point theorems | topological concepts
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Mathematics
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Metric spaces I
Preamble
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