Can a function from $(0,1)$ to $(0,1]$ be one-to-one and onto?
10458
How to define a bijection between $(0,1)$ and $(0,1]$?
103568
Possibility of finding a such function?
113687
$f$ is continuous function from $ [0,1]$ to itself and f(0)=0, f(1)=1 and $f(f(x))=x$ then show that $f(x)=x$ on$[0,1]$
53024
$f(x)f(1/x)=f(x)+f(1/x)$
57938
When do two functions become equal?
103625
Number of increasing functions from $\{1,2,\dots, n\}$ to itself.
85612
Let functions $ f: A \to B$ and $g: B \to A$, suppose that $ g \circ f = i_A$. Prove that if $f$ is onto, then $g$ is one-to-one
146306
A continuous surjective function from $(0,1]$ onto $[0,1]$
24306
Is there a continuous function $f(x)$ such that the inverse function is $1/f(x)$?
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
44689
Explicit bijection between $[0,1)$ and $(0,1)$
23728
Does a continuous and 1-1 function map Borel sets to Borel sets?
111477
Specify a bijection from [0,1] to (0,1].
11798
If $f \circ g$ is onto then $f$ is onto and if $f \circ g$ is one-to-one then $g$ is one-to-one
72642
Continuous bijection from $(a,b) \to S^1$?
100465
Does there exist a continuous bijection from $(-1,1) \to (-1,1]$?
124847
Is the set of surjective functions from $\mathbb{N}$ to $\mathbb{N}$ uncountable?