The Supremum and Bounded Functions
29849
How can I show that $\sup(AB)\geq\sup A\sup B$ for $A,B\subset\mathbb{R}$ where $A\cup B$ is positive and bounded?
97148
Does bounded variation imply boundedness
144530
is uniform convergent sequence leads to bounded function?
117257
Proving the supremum of the set {$\cos (1/x)$} is 1
125610
Space of bounded continuous functions is complete
55268
Differentiable and Continuous functions on [0,1] with 'weird' conditions.
41847
Uniformly continuous function with unbounded variation
9748
Maximum modulus principle for an unbounded function in the half right plane
7112
Product of sets and supremum
151410
Inequality of continuous functions
121079
lemma: Cauchy sequences are bounded.
75882
Countability of local maxima on continuous real-valued functions
72908
Bounding a strange function
24749
Monotone functions and Borel sets
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Continuous functions that attain local extrema at every point
36166
Uniform continuity on (0,1) implies boundedness
81203
Supremum and infimum of sets