About Density and continuous and open function.
67602
The inverse image of dense set is dense and of a comeager set is comeager?.
47498
Integration and theorems on continuous functions
17223
Continuity of an inverse function.
60070
Unique uniformly continuous function into complete space
140052
Show that $f(X - D) \cap f(D) = \varnothing$ with $f$ continuous in $X$, $D$ dense in $X$ and $f|_{D}$ homeomorphism
82280
Problem about continuous functions and the intermediate value theorem
128911
Continuous extension of a real function
29154
$f$ is continuous and open implies $f$ injective
127900
Interior of closure of open set in topological space
99858
Cumulative distribution function and right continuity
44574
Continuity of absolute value of a function
12240
Problem with a continuous function
130586
$f$ is discontinuous $\iff$ kernel($f$) is dense in X
115930
Is every convex function on an open interval continuous?
40576
Intermediate value property problem and continuous function
143174
property of continuous function
65346
Characterisation of uniformly continuous function