Each relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
- Relation ID
story_fundamental_group_to_covering_space_theorem_implication- Relation type
- Theorem implication
theorem-implication - Direction
- source β target
- Endpoint roles
- source: Implies by theorem; target: Follows by theorem from
- Authored annotation
- classifies connected coverings under standard hypotheses
Authored explanation
For a path-connected, locally path-connected, semilocally simply connected space, connected covering spaces correspond to conjugacy classes of subgroups of the fundamental group.
How to interpret this relation type
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
This is an authored directed relation from the source endpoint to the target endpoint.
- Relation ID
j_covering_space__out- Relation type
- Combine compatible structures
combine-compatible - Direction
- source β target
- Endpoint roles
- source: Builds toward; target: Built from
- Authored annotation
- impose local triviality
Authored explanation
Give E and B topologies and a continuous surjection p:EβB; require every point of B to have an evenly covered open neighborhood.
How to interpret this relation type
Feed several structures into a construction junction and impose compatibility between them.