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

Examples[edit]