Contruction: Bijective, continuous map from one topological space $X$ into itself that is not open
65034
Are continuous self-bijections of connected spaces homeomorphisms?
4538
Is the mapping $ d : X\times X \mapsto \mathbb {R} $ continuous?
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
41690
Products of Continuous functions: Topology
45276
Continuous map on $S^2$
27998
Prove existence of disjoint open sets containing disjoint closed sets in a topology induced by a metric.
37654
Topology: Example of a compact set but its closure not compact
25874
Showing that a certain map is not flat by explicit counterexample
113498
Example of topological spaces where sequential continuity does not imply continuity
38033
A surjective linear map into a finite dimensional space is open
101319
Properties of a continuous map $f : \mathbb{R}^2\rightarrow \mathbb{R}$ with only finitely many zeroes
115999
Is there always an injective map from a space in its dual space?
14322
Examples of bijective map from $\mathbb{R}^3\rightarrow \mathbb{R}$
15487
Continuous function from a connected set?
47251
Non-compactness of $\mathbb{R}$ with the cocountable topology
145077
A continuous bijection $f:\mathbb{R}\to \mathbb{R}$ is an homeomorphism?
50649
On the existence of a continuous bijection $f\colon [0,1]\to [0,1]\times [0,1]$