Continuous bijective function between the same topology that is not a homeomorphism.
65034
Are continuous self-bijections of connected spaces homeomorphisms?
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
113498
Example of topological spaces where sequential continuity does not imply continuity
77563
Homeomorphism between spaces equipped with cofinite topologies
7036
Is there a bijective continuous function $f: \Bbb R \to \Bbb R$ whose inverse $f^{-1}$ is not continuous?
136538
How can I show that a bijection between $[0,1)$ and $(0,1)$ cannot be continuous?
70645
Borel set preserved by continuous map
132571
Local homeomorphisms which are not covering map?
111689
Surjective, but not injective endomorphism
15487
Continuous function from a connected set?
66180
Homomorphism between compact Hausdorff spaces.
32359
Inner product of two continuous maps is continuous
111246
product of two continuous proper maps
95086
Homeomorphism is bijective
62817
Functions which are Continuous, but not Bicontinuous
64375
Non-Metrizable Topological Spaces