Locally connected space
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In topology and related branches of mathematics, a locally connected space is a topological space that has a base of connected sets. That is, every neighbourhood of every point of the space contains a neighbourhood that is both open and connected.
[edit] Examples
- The space
- <math>(-2, -1) \cup (1, 2) \subsetneq \mathbb{R}</math>
with the subspace topology induced from the usual topolgy on the real line is locally connected but not connected.
- The topologist's sine curve is an example of a connected space that is not locally connected.
