Locally connected not implies locally path-connected

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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 (?)) need not satisfy the second topological space property (i.e., Locally path-connected space (?))
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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


Locally path-connected implies locally connected

Other related facts


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