Show that $\mathbb{R} \times X \to X: (\lambda, x ) \mapsto \lambda x$ is continuous
53850
Proof that every normed vector space is a topological vector space
6161
The cartesian product $\mathbb{N} \times \mathbb{N}$ is countable
2198
Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
126461
Show that $g:I\to\mathbb{R}$ is continuous and $f:(x-x_0)g(x)$ is differentiable
31548
Proof of "every convex function is continuous"
57023
If $f,g$ are continuous at $a$, show that $h(x)=\max\{f(x),g(x)\}$ and $k(x)=\min\{f(x),g(x)\}$ are also continuous at $a$
145368
How to show $f:Y\to X^{+}$ is continuous?
73469
Continuity of the function $x\mapsto d(x,A)$ on a metric space
77621
Continuity of function mapping connected set to connected set
58664
Proving a function is continuous for a fixed variable
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.
36227
Show continuity or uniform continuity of $\phi: (C([0,1];\Bbb R ),||\cdot||_\infty )\to (\Bbb R, |\cdot | )$
121957
Is $p\mapsto \|f\|_p$ continuous?
72644
Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?
12349
a construction of a continuous function from a normal space to [0,1]
41690
Products of Continuous functions: Topology
75479
Proving that this function is continuous on $G\times G$