Continuous maps vs. open maps
67948
Why are continuous functions the "right" morphisms between topological spaces?
25874
Showing that a certain map is not flat by explicit counterexample
111710
intutive difference between linear map/transformation vs linear function
153952
A map between metric spaces preserving convergent sequences is continuous
70048
In which topologies do open sets maintain open under countable or arbitrary intersection?
92870
composition of covering maps
154259
Countinuity of the identity map between different topologies
12490
A map is continuous if and only if for every set, the image of closure is contained in the closure of image
137460
How should I think of an open vs. closed set?
48419
Difference between $\mathbb{R}$-linear and $\mathbb{C}$-linear maps
117897
A homomorphism induces a continuous map from ${\rm Spec}(A') \to {\rm Spec}(A)$.
35804
Bi-Lipschitz map preserves completeness
47992
Is there a function $f\colon\mathbb{R}\to\mathbb{R}$ such that every non-empty open interval is mapped onto $\mathbb{R}$?
47
Let $f$ be a continuous and open map from $\mathbb R $ to $\mathbb R$.Prove that $f$ is monotonic.
158221
Prob. 4 (a), Sec. 20 in Munkres' Topology, 2nd ed: Are these functions continuous in the product, uniform, and box topologies?
36149
A uniformly continuous function maps bounded set to bounded sets
152493
Is an expanding map on a compact metric space continuous?