# Locally connected not implies locally path-connected

From Topospaces

This article gives the statement and possibly, proof, of a non-implication relation between two topological space properties. That is, it states that every topological space satisfying the first topological space property (i.e., Locally connected space (?)) neednotsatisfy the second topological space property (i.e., Locally path-connected space (?))

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## Contents

## Statement

It is possible for a [[topological space] to be a locally connected space but *not* a locally path-connected space.

## Definitions used

### Locally connected space

`Further information: locally connected space`

### Locally path-connected space

`Further information: locally path-connected space`

## Related facts

### Converse

Locally path-connected implies locally connected

- Connected not implies path-connected
- Connected and locally path-connected implies path-connected
- Path-connected implies connected

## Proof

*Fill this in later*