Article | REF: AF121 V1

Metric Spaces II. Special Spaces

Author: Jean-Charles PINOLI

Publication date: July 10, 2018, Review date: May 7, 2021

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ABSTRACT

General topology is the branch of mathematics that deals with the fundamental concepts of boundary, continuity and neighborhood 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 deals with specific topological and metric spaces, spaces of maps between metric spaces, and space subsets of a given metric space.

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AUTHOR

  • 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 [AF97][AF98] focusing on topological spaces, the next two [AF120] [AF121] on metric spaces, and the last two [AF122][AF123] detailing almost 150 examples of topological/metric spaces with or without the various topological/metric notions presented in the aforementioned articles.

Reading the two articles in the series on topological spaces [AF97] and [AF98] is not a prerequisite, but is recommended. The reader can refer to them to consult one or more particular points.

The reader is invited to read section 1 of the article

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KEYWORDS

subset spaces   |   topological concepts   |   spaces of maps   |   object spaces


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