Show that a CW complex is path-connected if and only if its 1 skeleton is path- connected (taken from Hatcher's Algebraic Topology appendix)
Added by Rwejuna A.
Step 1
Recall that each n-cell e^n has a characteristic map Φ: D^n → X whose restriction to int(D^n) is a homeomorphism onto e^n and whose restriction to S^{n-1}=∂D^n is the attaching map S^{n-1} → X^{n-1}. Also X = ⋃_{n≥0} X^n. Show more…
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