isSimplyConnected
P22987
predicate
Indicates that a topological space has no "holes," meaning every loop within it can be continuously contracted to a single point.
All labels observed (3)
| Label | Occurrences |
|---|---|
| isSimplyConnected canonical | 14 |
| hasFundamentalGroup | 11 |
| simplyConnected | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: isSimplyConnected
Generated description
Indicates that a topological space has no "holes," meaning every loop within it can be continuously contracted to a single point.
Sample triples (26)
| Subject | Object |
|---|---|
| Euclidean space | true ⓘ |
| SU(3) | true ⓘ |
| SU(3) | trivial group via predicate surface "hasFundamentalGroup" ⓘ |
| SL(2,C) | true ⓘ |
| SL(2,C) | trivial via predicate surface "hasFundamentalGroup" ⓘ |
| Riemann sphere | true ⓘ |
|
rotation group SU(2)
surface form:
SU(2)
|
true ⓘ |
|
rotation group SU(2)
surface form:
SU(2)
|
trivial group via predicate surface "hasFundamentalGroup" ⓘ |
|
rotation group SU(2)
surface form:
SO(3)
|
Z/2Z via predicate surface "hasFundamentalGroup" ⓘ |
| U(1) | Z via predicate surface "hasFundamentalGroup" ⓘ |
| orthogonal group O(n+1,2) | ℤ for n+3 ≥ 3 (via SO⁰(n+1,2)) via predicate surface "hasFundamentalGroup" ⓘ |
|
special linear group SL(n,R)
surface form:
SL(n,ℝ)
|
ℤ for n = 2 via predicate surface "hasFundamentalGroup" ⓘ |
|
special linear group SL(n,R)
surface form:
SL(n,ℝ)
|
false for n ≥ 2 ⓘ |
| Spin(2,d) | true ⓘ |
|
general linear group GL(n,C)
surface form:
GL(n,ℂ)
|
false ⓘ |
|
special linear group SL(n,C)
surface form:
SL(n,ℂ)
|
true for n ≥ 2 ⓘ |
|
special linear group SL(n,C)
surface form:
SL(n,ℂ)
|
0 (trivial) for n ≥ 2 via predicate surface "hasFundamentalGroup" ⓘ |
| PSL(2,ℝ) | false ⓘ |
| Poincaré upper half-plane model | true ⓘ |
| SL(2,R) | false via predicate surface "simplyConnected" ⓘ |
|
PSL(2,\mathbb{C})
surface form:
PSL(2,ℂ)
|
ℤ/2ℤ via predicate surface "hasFundamentalGroup" ⓘ |
|
PSL(2,\mathbb{C})
surface form:
PSL(2,ℂ)
|
false ⓘ |
| Teichmüller space | true ⓘ |
|
Hurwitz surfaces
surface form:
Hurwitz surface
|
torsion-free subgroup of (2,3,7) triangle group via predicate surface "hasFundamentalGroup" ⓘ |
| 4-sphere S^4 | true ⓘ |
|
Seifert fibered spaces
surface form:
Seifert fibered space
|
group fitting into short exact sequence with Z as normal subgroup via predicate surface "hasFundamentalGroup" ⓘ |