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dimension of a separable metric space

Contents

Context

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Contents

Definition

The dimension of a separable metric space is taken to be its covering dimension, which coincides with its (small and large) inductive dimension (e.g., Engelking 78, Theorem 1.7.7)

notion of dimension

References

  • Ryszard Engelking, Dimension Theory, Mathematical Library 19, North-Holland Publishing/Polish Scientific Publishers 1978 (pdf)

  • Ryszard Engelking, Theory of Dimensions – Finite and Infinite, Sigma Series in Pure Mathematics 10, Helderman 1995 (pdf)

Last revised on March 21, 2021 at 11:12:02. See the history of this page for a list of all contributions to it.