Is the mapping $ d : X\times X \mapsto \mathbb {R} $ continuous?
53812
Metric is continuous function
65472
From injective map to continuous map
60692
Is this map to a finite dimensional topological vector space an open map?
150770
Why is $f^n(\xi(x))$ continuous over $x$?
138784
Is the differentiation operator an open mapping?
121957
Is $p\mapsto \|f\|_p$ continuous?
103932
How can I prove that a polynomial with degree $n$ is continuous everywhere in $\mathbb{R}$ using definitions?
124535
continuous function from $[\pi,2\pi]\to \mathbb{R}^2$
9320
Extension of continuous function on a closed subset of $\mathbb{R}$
67234
The function $G: x \mapsto 2^{x^2}$ maps $\mathbb{R}$ onto $\{ x \in \mathbb{R} : x \geq 1 \}$
72644
Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?
140052
Show that $f(X - D) \cap f(D) = \varnothing$ with $f$ continuous in $X$, $D$ dense in $X$ and $f|_{D}$ homeomorphism
52388
The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition
111246
product of two continuous proper maps
32359
Inner product of two continuous maps is continuous
153495
Continuous function does not map closed set to closed set
156996
Do there exist general conditions under which we can conclude that continuity on a topological space is detected by $\mathbb{R}$?