[alg.top]

Cell complexes are always path-connected.

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[alg.top]

Cell complexes are always path-connected.

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[alg.top]

Standard (cubic lattice) CW complex structure on : Lattice of 0-cells, join all by 1-cells, then add 2-cells, 3-cells etc.

Check this rigorously.

[alg.top]

contractible deformation retracts to a point

But the converse is true?