Prove $T$ continuous if and only if $T$ bounded.
140813
How do i prove that continuous linear transformation between normed spaces is bounded?
158349
Prove the map sending a matrix to it's inverse is continuous.
58664
Proving a function is continuous for a fixed variable
153957
Bounded variation and $\int_a^b |F'(x)|dx=T_F([a,b])$ implies absolutely continuous
19111
If every real-valued continuous function is bounded on $X$ (metric space), then $X$ is compact.
131992
A problem on continuous functions
83831
Continuity based on restricted continuity of two subsets
15579
Show that $f$ is uniformly continuous if limit exists
51156
Function is Continuous When Restricted to Closed Sets Which Cover the Space
12408
Prove that a function whose derivative is bounded is uniformly continuous.
93021
$f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$
30965
$f$ is continuous on $X$ iff $f$ is continuous on every compact subset
13852
Assume $f$ is a continuous one-to-one function over an interval. Prove that $f$ is strictly monotone
62118
Prove $\epsilon$-$\delta$ definition of continuity implies the open set definition for real function
53349
Prove that $\sqrt{x}$ is continuous on its domain $[0, \infty).$
113122
Prove that a continuous real function with finite limits is bounded
100740
proof of that a continuous function has a fixed point