homeomorphicTo
P73738
predicate
Indicates that two topological spaces can be continuously deformed into each other via a bijective, continuous map with a continuous inverse, preserving their topological structure.
Observed surface forms (4)
- isHomeomorphicTo ×7
- topologicallyEquivalentTo ×3
- isNotHomeomorphicTo ×1
- topologicallyHomeomorphicTo ×1
Sample triples (14)
| Subject | Object |
|---|---|
| Baire space | irrational numbers with the usual topology via predicate surface "isHomeomorphicTo" ⓘ |
| Baire space | set of all functions from N to N with product topology via predicate surface "isHomeomorphicTo" ⓘ |
| Baire space ω^ω | Cantor space 2^ω via predicate surface "isNotHomeomorphicTo" NERFINISHED ⓘ |
| Baire space ω^ω | set of irrationals in ℝ with the subspace topology via predicate surface "isHomeomorphicTo" ⓘ |
| Baire space ω^ω | space of all functions from ω to ω with the topology of pointwise convergence from discrete ω via predicate surface "isHomeomorphicTo" ⓘ |
| Baire space ω^ω | space of all strictly increasing sequences of natural numbers via predicate surface "isHomeomorphicTo" ⓘ |
| Baire space ω^ω | ω^ω with the Baire metric via predicate surface "isHomeomorphicTo" ⓘ |
| Cantor set |
Cantor set
self-linksurface differs
ⓘ
surface form:
Cantor space {0,1}^N with product topology
|
| Cantor set | product of countably many discrete two-point spaces ⓘ |
| Riemann sphere | 2-sphere via predicate surface "topologicallyEquivalentTo" ⓘ |
| Riemann sphere | unit sphere in \mathbb{R}^3 via predicate surface "topologicallyEquivalentTo" ⓘ |
|
rotation group SO(3)
surface form:
SO(3)
|
RP³ via predicate surface "topologicallyHomeomorphicTo" ⓘ |
| U(1) | S^1 via predicate surface "isHomeomorphicTo" ⓘ |
| van Kampen diagram | disc diagram via predicate surface "topologicallyEquivalentTo" ⓘ |