User:Juan Marquez/ends
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The concept on end of a space is important because belongs to a serie of invariants called quasi-isometry
ends of a group
[edit]A subset's relation , with symbol , called almost-inclusion and almost-equality in the power set of a group is defined as
- means that is a finite set
- means that and
A subset is dubbed almost-invariant if and only if
- for each it happens
The set together with the symmetric difference is -vector space and it have the subspaces
- is almost-invariant
- is finite
then the number of ends happens to be equals to the dimension of