counterexample in topology
15546
Connected But Not Path-Connected?
19984
Example of topological spaces with continuous bijections that are not homotopy equivalent
51871
Characterization of Topology
114856
Universal property of initial topology
18125
Counterexamples to the converse to Lagrange's Theorem different from $A_{4}$.
114773
counterexamples on modules
100121
Assume that $(\text{X}, T)$ is compact and Hausdorff. Prove that a comparable but different topological space $(\text{X},T')$ is not.
137621
The Number of Topologies on a Finite Set
76572
What facts about the weak topology fail in spaces that aren't Banach?
147793
A variation on the induced topology (subspace topology)
70048
In which topologies do open sets maintain open under countable or arbitrary intersection?
69204
When I prove two topologies are same, is it sufficient to prove they have same basis? If so,Why?
122352
Topologies in a Riemannian Manifold
158221
Prob. 4 (a), Sec. 20 in Munkres' Topology, 2nd ed: Are these functions continuous in the product, uniform, and box topologies?
77297
Counterexample for $A,B\triangleleft G,G/A\cong B \Rightarrow G/B\cong A$
130361
Basis for a topology with a countable number of sets
77563
Homeomorphism between spaces equipped with cofinite topologies