Is the function from $\mathbb{R}$ to $\mathbb{R}$ that maps every compact set to compact set and connected set to connected set continuous?
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
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 $X$ ?
105652
Suppose $f: \mathbb{R} \to \mathbb{R}$ is function such that $f^3$ is continuous on $\mathbb{R}$. Prove that $f$ is continuous on $\mathbb{R}$
135863
Is the graph of a continuous function homeomorphic to its domain?
73594
Existence of continuous function $f$ on $\Bbb R$ which vanishes exactly on $A\subset \Bbb R$
145077
A continuous bijection $f:\mathbb{R}\to \mathbb{R}$ is an homeomorphism?
14495
I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$
107148
Does there always exist a continuous/smooth map from $\mathbb{R}^n$ onto a manifold $M^n$?
63598
Is every separately continuous function on $R^2$ continuous?
67948
Why are continuous functions the "right" morphisms between topological spaces?
111990
Continuous function from $(0, 1]$ onto $(0, 1)$?
79107
Give an example of a function $f: \mathbb{R} \to \mathbb{R}$ which is continuous only at $0$.
136583
Infimum is a continuous function, compact set
47251
Non-compactness of $\mathbb{R}$ with the cocountable topology
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
155794
Are the complements of two homeomorphic compact, connected subsets of $\mathbb{R}^2$ homeomorphic?
158221
Prob. 4 (a), Sec. 20 in Munkres' Topology, 2nd ed: Are these functions continuous in the product, uniform, and box topologies?