Proving that $f(\bar Z)\subset\overline {f(Z)}$ when $f$ is a continuous map
12490
A map is continuous if and only if for every set, the image of closure is contained in the closure of image
32359
Inner product of two continuous maps is continuous
45276
Continuous map on $S^2$
128069
Continuity in Slices + Mapping Compact Sets to Compact Sets = Continuous
34836
Composition of Absolutely Continuous Functions
83046
A linear map, continuous at zero, is bounded
21921
Showing that $|f(z)| \leq \prod \limits_{k=1}^n \left|\frac{z-z_k}{1-\overline{z_k}z} \right|$
30455
Show that any continuous $f:[0,1] \rightarrow [0,1]$ has a fixed point $\zeta$
4538
Is the mapping $ d : X\times X \mapsto \mathbb {R} $ continuous?
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
101319
Properties of a continuous map $f : \mathbb{R}^2\rightarrow \mathbb{R}$ with only finitely many zeroes
31747
Uniqueness of continuous extension from $A$ to $\overline{A}$ for maps into a Hausdorff space
28637
Proving continuous image of compact sets are compact
149354
Proof of continuity $f(x+y) = f(x) + f(y)$
23617
Determine whether $f(x)={\sin x \over x}$ is uniformly continuous in $\mathbb R$
52388
The equivalence of open-set definition of continuous mappings to the $\epsilon-\delta$ definition