Continuous function and normal topological space
12349
a construction of a continuous function from a normal space to [0,1]
131992
A problem on continuous functions
140052
Show that $f(X - D) \cap f(D) = \varnothing$ with $f$ continuous in $X$, $D$ dense in $X$ and $f|_{D}$ homeomorphism
97761
Show that a proper continuous map from $X$ to locally compact $Y$ is closed
64487
Continuous function and dense set
136011
Must $f$ be continuous?
60070
Unique uniformly continuous function into complete space
110832
$F_\sigma$-subsets in a normal space can be separated
46287
Let $Y$ be an ordered set in the order topology with $f,g:X\rightarrow Y$ continuous, show that $\{x:f(x)\leq g(x)\}$ is closed in $X$
55238
Show that if $f:X\to Y$ is a continuous function if and only if the graph of $f$ is a closed subset of $X\times Y$
153495
Continuous function does not map closed set to closed set
51156
Function is Continuous When Restricted to Closed Sets Which Cover the Space
74364
Show that function $f$ has a continuous extension to $[a,b]$ iff $f$ is uniformly continuous on $(a,b)$
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 $X$ ?
99179
Continuous function with compact domain has continuous inverse
153256
Compact topological space with closed graph implies continuity
83326
$f:\mathbb R\to\mathbb R$ continuous function. Which of the following sets can not be image of $(0,1]$ under $f$?