|
|
| Line 1: |
Line 1: |
| {{homology-dependent topospace property}}
| | #redirect [[Space with homology of finite type]] |
| | |
| ==Definition==
| |
| | |
| A [[topological space]] is said to have '''finitely generated homology groups''' if all its homology groups are finitely generated. Note that the condition of being a [[space with finitely generated homology]] is significantly stronger: it requires that there should also be only finitely many nonzero homology groups.
| |
| | |
| ==Relation with other properties==
| |
| | |
| ===Stronger properties===
| |
| | |
| * [[Space with finitely generated homology]]
| |
| | |
| ===Incomparable properties===
| |
| | |
| * [[Space with finitely generated homotopy groups]]
| |
| * [[Space with homology of finite type]]
| |