Intuition to understanding why homotopic attaching maps of n-cell yield homotopy equivalent space
124829
Prove homotopic attaching maps give homotopy equivalent spaces by attaching a cell
147752
Is the quotient map a homotopy equivalence?
133413
Proof of paracompactness of CW-complexes (J. Lee, Introduction to Topological Manifolds)
59289
Nested Sequence of Topological Space and the Coherent Topology; Munkres Topology 35.9
77175
Proof that two spaces that are homotopic have the same de Rham cohomology
147961
Characterizing simply connected spaces
76563
Category Theory usage in Algebraic Topology
18687
First and second homotopy groups of a connected Lie group
136202
Is a loop in $X$ based at $a\in X$ homotopic to its reverse loop?
44069
Proof that a continuous map to $S^n$ whose image is a proper subset of $S^n$ is null-homotopic
77563
Homeomorphism between spaces equipped with cofinite topologies
120100
Hairy Ball Theorem: homotopy from the identity to the antipodal map
5540
Why aren't these loops homotopic?
147793
A variation on the induced topology (subspace topology)
94165
Why is a map to a smaller dimensional space not injective?
92340
How many metrics are there on a set up to topological equivalence?
108864
Showing that two topologies give rise to the same topology