Locally connected not implies locally path-connected
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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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
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