Prove functions defined by sup and inf are continuous
12523
Supremum of a Continuous Function is Continuous
40297
Proof of uniform limit of Continuous Functions
113871
Prove $f(x) = \sqrt x$ is uniformly continuous on $[0,\infty)$
46834
show that a distance function is continuous
130023
Prove that the sum of two continuous functions is continuous
53627
Proving continuity of $f$
78463
Prove that $\sup \{-x \mid x \in A\} = -\inf\{x\mid x \in A\}$
134752
Proof (epsilon delta) for the continuity of a function at a point
113122
Prove that a continuous real function with finite limits is bounded
125682
Proof verification: the product of two continuous functions is continuous
77944
Injective functions with intermediate-value property are continuous. Better proof?
136789
How to prove $a \lt b$ for all $a \in A, b \in B$ implies $\sup A \leq \inf B$?
100187
Show function is continuous at origin
88603
verify equicontinuous functions
53738
Monotone functions and continuity
88240
Two functions discontinuous, but sum continuous
97772
An example of a function which satisfies $\sup_{y}\inf_{x}f(x,y)<\inf_{x}\sup_{y}f(x,y)$