The simply connected coverings of two homotopy equivalent spaces are homotopy equivalent
32923
Homotopy equivalence of universal cover
139779
Homotopic maps have homotopy equivalent mapping cones
76040
Show that the Euler characteristic of a chain complex is equal to the Euler characteristic of its homology
42811
Product of path connected spaces is path connected
112607
Why is homology invariant under deformation retraction/homotopy equivalence?
110729
Maps to Sn homotopic
20692
Homotopy groups of a wedge sum
42913
Equivalence of the definition of the Subbasis of a Topology
120100
Hairy Ball Theorem: homotopy from the identity to the antipodal map
95187
The set of homotopy classes
147961
Characterizing simply connected spaces
82814
Homework question on whether two quotient spaces are homeomorphic
52729
Homotopic maps $(X, A) \to (Y, B)$ induce homotopic maps $X/A \to X/B$
92870
composition of covering maps
150987
Showing that the product and metric topology on $\mathbb{R}^n$ are equivalent
16512
Product of $T_1$ spaces is $T_1$
77175
Proof that two spaces that are homotopic have the same de Rham cohomology