General topology Connectedness Concept
Path-connected space
Summary
A topological space is path-connected when any two of its points can be joined by a continuous path. Path-connected spaces are connected, but the converse is false.
Where this leads
14 pages build on this one.
- Warsaw circle
- Locally path-connected space
- Hawaiian earring
- Comb space
- Long exact sequence of homotopy groups
- Universal cover
- n-connected space
- Postnikov tower
- Galois correspondence for coverings
- Seifert–van Kampen theorem
- Eilenberg–MacLane space
- Classification of covering spaces
- Hurewicz theorem
- Whitehead tower
Further reading
- Web https://en.wikipedia.org/wiki/Connected_space, Path connectedness
About this page
| Tag | 0WB6DH499T |
|---|---|
| URI | m2://0WB6DH499T |
| Aliases | pathwise-connected-space |
| Kind | concept |
| Writing | W1 stated |
| MSC | 54D05 |
| Specializes | Connected space |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Definitions
Used by
- Warsaw circle
- Locally path-connected space
- Hawaiian earring
- Comb space
- Long exact sequence of homotopy groups
- Universal cover
- n-connected space
- Postnikov tower
- Galois correspondence for coverings
- Seifert–van Kampen theorem
- Eilenberg–MacLane space
- Classification of covering spaces
- Hurewicz theorem
- Whitehead tower