Permute supremum and limit in the upper semicontinuous case
136583
Infimum is a continuous function, compact set
87239
Prove functions defined by sup and inf are continuous
48593
Proof that if $s_n \leq t_n$ for $n \geq N$, then $\liminf_{n \rightarrow \infty} s_n \leq \liminf_{n \rightarrow \infty} t_n$
141366
Absolutely continuity and Lipschitz-like continuity
41847
Uniformly continuous function with unbounded variation
60520
Upper bound for $|f(0)|$ based on its behavior within the unit disk.
133886
Existence of increasing sequence $\{x_n\}\subset S$ with $\lim_{n\to\infty}x_n=\sup S$
128482
The set of subsequential limits is closed
1521
Supremum and Infimum
66824
Two definitions of $\limsup$
7112
Product of sets and supremum
142232
Functional Analysis. Continuous extensions of linear functionals.
155999
How to prove the following properties of infimum and supremum involving the union and intersection of the sets $A_k$
72185
The negation of a limit condition, Spivak style.
129757
Uniformly convergent implies equicontinuous
3023
Construction of a Borel set with positive but not full measure in each interval
22558
Vitali-type set with given outer measure