$f:X\to Y$ and $g:Y\to X$ are bijective and continuous. Then two metric spaces $X$ and $Y$ are homeomorphic?
112306
Two manifolds $X$ and $Y$ with two bijective continuous functions from $X$ to $Y$ and $Y$ to $X$, but not homeomorphic
21269
Bijective continuous function between $(0 ,\infty)$ and $\mathbb{R}$.
29154
$f$ is continuous and open implies $f$ injective
32340
Continuous bijections and their inverses
33114
Uniqueness of a continuous extension of a function into a Hausdorff space
67948
Why are continuous functions the "right" morphisms between topological spaces?
53812
Metric is continuous function
15480
Open set in a metric space is union of closed sets
41690
Products of Continuous functions: Topology
60236
What is the difference between topological and metric spaces?
83446
bijective continuous function on $\mathbb R^n$ not homeomorphism?
118851
$X$ be a Hausdorff topological space , let $f:X \to X$ be a continuous map such that $f\circ f=f$ , then is $f(X)$ is closed in $X$ ?
101773
Let $g : A \to B$ and $f : B \to C$ be functions. Let $f \circ g$ be onto. Are both $f$ and $g$ necessarily onto?
44402
If $\{x:f(x) > a\}$ and $\{x:f(x) < a\}$ are open$\forall~a\in\mathbb{R}$ then f is continuous.
65034
Are continuous self-bijections of connected spaces homeomorphisms?
72642
Continuous bijection from $(a,b) \to S^1$?
72251
$g\circ f$ is Surjective and $g$ is Injective then Prove that $f$ is surjective