Contents

# Contents

## Definition

Given a topological space $X$, then a set of subset $\{S_i \subset X\}_{i \in I}$ is locally discrete if every point $x \in X$ has a neighborhood which intersects at most one of the $S_i$.

Often one can find a base of a topological space that decomposes into a countable union of locally discrete sets. In this case the base is called $\sigma$-discrete. Such a base can be found for any metric space.

## References

• Ryszard Engelking, General Topology, Heldermann Verlag Berlin, 1989.

• K. Kuratowski, Topology, 2014, vol. 1.

Last revised on April 10, 2019 at 04:18:20. See the history of this page for a list of all contributions to it.