Contents

# Contents

## Idea

In topology, a separable metric space is a topological space that is both separable and metrizable.

## Properties

### Dimension

###### Proposition

For separable metric spaces, the following notions of dimension all (exist and) coincide and are thus uniformly referred to as the dimension of a separable metric space:

1. small and large inductive 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 10:51:02. See the history of this page for a list of all contributions to it.