Counter-example of function which is continuous on closed subspaces, but not continuous on whole space
65196
Gluing Lemma for Closed Sets: Infinite Cover Counter-Example
2118
Are continuous functions with compact support bounded?
58816
Existence of a continuous function which does not achieve a maximum.
99179
Continuous function with compact domain has continuous inverse
113450
Construction of a function which is not the pointwise limit of a sequence of continuous functions
30036
Function in $H^1$, but not continuous
115794
When is the vector space of continuous functions on a compact Hausdorff space finite dimensional?
33140
Two non-homeomorphic spaces with continuous bijective functions in both directions
158221
Prob. 4 (a), Sec. 20 in Munkres' Topology, 2nd ed: Are these functions continuous in the product, uniform, and box topologies?
143174
property of continuous function
133696
Example of a function continuous at only one point.
91682
Graph of a continuous function is closed
123132
Counterexample for a non-measurable function?
87983
Examples of Separable Spaces that are not Second-Countable
65876
A normed space of continuous functions with norm $\int_{0}^{1}|f(t)|dt$ is not complete
53738
Monotone functions and continuity
52798
Finding counterexamples: bijective continuous functions that are not homeomorphisms