# Definition:Locally Connected Space/Definition 2

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## Definition

A topological space $T = \struct{S, \tau}$ is **locally connected** if and only if $T$ is weakly locally connected at each point of $T$.

That is, a topological space $T = \struct{S, \tau}$ is **locally connected** if and only if each point of $T$ has a neighborhood basis consisting of connected sets of $T$.

## Also see

## Sources

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- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**locally connected**

This page may be the result of a refactoring operation.As such, the following source works, along with any process flow, will need to be reviewed. When this has been completed, the citation of that source work (if it is appropriate that it stay on this page) is to be placed above this message, into the usual chronological ordering.If you have access to any of these works, then you are invited to review this list, and make any necessary corrections.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{SourceReview}}` from the code. |

- 1975: Bert Mendelson:
*Introduction to Topology*(3rd ed.): $\S 4.5$: Components and Local Connectedness: Definition $5.8$ and Lemma $5.10$