Show that mapping cones are homotopy equivalent.
139779
Homotopic maps have homotopy equivalent mapping cones
52354
Given a idempotent endomorphism, show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$
124829
Prove homotopic attaching maps give homotopy equivalent spaces by attaching a cell
117897
A homomorphism induces a continuous map from ${\rm Spec}(A') \to {\rm Spec}(A)$.
65472
From injective map to continuous map
115347
Showing that the fiber of a morphism of schemes over a point is homeomorphic to the preimage
133413
Proof of paracompactness of CW-complexes (J. Lee, Introduction to Topological Manifolds)
104881
Showing that two Banach spaces are homeomorphic when their dimensions are equal.
14322
Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$
62711
Canonical map $R/(I\cap J)\rightarrow R/I\times _{R/(I+J)} R/J$ is an isomorphism
44069
Proof that a continuous map to $S^n$ whose image is a proper subset of $S^n$ is null-homotopic
101064
Showing the triviality of homomorphisms
39010
Metrization of the cofinite topology
108045
Show that are logically equivalent
25874
Showing that a certain map is not flat by explicit counterexample
15312
Show that $R \cap R^{−1}$ is an equivalence relation on $X$?
116732
Proving that a continuous map is surjective