Proof that $f$ is continuous if and only if $f$ composed with projections is continuous
109423
Purpose of universal property of a product.
15579
Show that $f$ is uniformly continuous if limit exists
128069
Continuity in Slices + Mapping Compact Sets to Compact Sets = Continuous
57180
Techniques to prove a function is uniformly continuous
22597
Composition of measurable function and continuous function
145368
How to show $f:Y\to X^{+}$ is continuous?
135661
Weakly continuous operators are continuous
87239
Prove functions defined by sup and inf are continuous
23436
$f$ Holder continuous with Holder exponent $p>1\implies f \text{ is constant}$
64619
Continuity of a function of product spaces
155618
Slightly changing the formal definition of continuity of $f: \mathbb{R} \to \mathbb{R}$?
90619
For closed subsets $A,B \subseteq X$ with $X = A \cup B$ show that $f \colon X \to Y$ is continuous iff $f|_A$ and $f|_B$ are continuous.
132869
Show that any bounded linear functional on a normed linear space is continuous
154559
For each $x\in X$ there exists a neighborhood of x s.t $A\cap U\neq \emptyset$ for only finitely many $A\in\mathcal{A}$. Show that f is continuous.
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
145919
If $f: \Bbb{R}\rightarrow\Bbb{R}$ is continuous at $0$ and $f(x)=f(2x)$ for each $x\in\Bbb{R}$ then $f$ is constant.
71487
Real Analysis: Continuity of a Composition Function