Weakly contractible not implies contractible
From Topospaces
This article gives the statement and possibly, proof, of a nonimplication relation between two topological space properties. That is, it states that every topological space satisfying the first topological space property need not satisfy the second topological space property
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Contents
Statement
It is possible for a topological space to be a weakly contractible space but not a contractible space.
Definitions used
Weakly contractible space
Further information: weakly contractible space
A topological space is termed weakly contractible if it is a pathconnected space and all its homotopy groups are trivial.
Contractible space
Further information: contractible space
A topological space is termed contractible if it is homotopyequivalent to a point.
Proof
Further information: double comb space
The double comb space is an exampe of a weakly contractible space that is not contractible. This is a subset of the Euclidean plane equipped with the subspace topology. Fill this in later