weak homotopy equivalence
A continuous map between path-connected based topological spaces is said to be a weak homotopy equivalence if for each it induces an isomorphism between the th homotopy groups. and are then said to be weakly homotopy equivalent.
It is not enough for to be isomorphic to for all The definition requires these isomorphisms to be induced by a space-level map
More generally, two spaces and are defined to be weakly homotopy equivalent if there is a sequence of spaces and maps
in which each map is a weak homotopy equivalence.
|Title||weak homotopy equivalence|
|Date of creation||2013-03-22 13:25:45|
|Last modified on||2013-03-22 13:25:45|
|Last modified by||antonio (1116)|
|Defines||weakly homotopy equivalent|