How to prove the induced map; $g_* : C(Y) \rightarrow C(X)$, induced from the map $g \in C(X, Y)$, endowed with fine topology is an embedding.
133422
How to prove the continuity of an induced map; $g_* : C(X, Y) \rightarrow C(X, R)$, induced from the map $g \in C(Y, R)$, endowed with fine topology.
46788
Compact open topology on space of continuous maps from a discrete space is a product
105666
What's an easy way to show that $GL(n,\mathbb C)$ is connected?
41035
Mapping that proves $\mathbb{Z} \subset \mathbb{Q}$
150987
Showing that the product and metric topology on $\mathbb{R}^n$ are equivalent
42941
Pair of adjoint functors and showing that two certain maps are inverses
78513
Show finite complement topology is, in fact, a topology
18034
Is there an equivalence relation of which the quotient topology is homeomorphic to codomain of a quotient map?
117897
A homomorphism induces a continuous map from ${\rm Spec}(A') \to {\rm Spec}(A)$.
67383
Prove that $G'$ is not planar.
102084
How to show path-connectedness of $GL(n,\mathbb{C})$
116768
Problem 5, sec. 13 in Munkres' Topology, 2nd ed.: How to prove the assertion if $\mathscr{A}$ is a subbasis?
147793
A variation on the induced topology (subspace topology)
59289
Nested Sequence of Topological Space and the Coherent Topology; Munkres Topology 35.9
18039
Let $A$ be a dense subset of $X$ and suppose $A$ is connected in the induced subspace topology, then $X$ is also connected
47251
Non-compactness of $\mathbb{R}$ with the cocountable topology
2575
Showing that $\mathbb{R}$ is connected