How to prove: if $f$ is continuous on $[a,b]$, then $f$ is bounded on $[a,b]$
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Real function continuous on closed interval implies it is bounded - over-simple proof??
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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 $a$
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$f$ is bounded and continious $\Rightarrow$ the convolution integral $\int f(\tau)g(x-\tau)\text{ d}\tau$ is bounded and continuous
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$f \in {\mathscr R[a,b]} \implies f $ has infinitely many points of continuity.
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Prove that a continuous real function with finite limits is bounded
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Show that f(x) defined on [0,infinity) R to is continuous at 0.
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$f$ is continuous and open implies $f$ injective
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Bounded variation and $\int_a^b |F'(x)|dx=T_F([a,b])$ implies absolutely continuous
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proof $f(\overline{A})\subseteq \overline{f(A)} \Leftrightarrow f$ continuous
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Proving that if $f: \mathbb{C} \to \mathbb{C} $ is a continuous function with $f^2, f^3$ analytic, then $f$ is also analytic
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let $f \colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ and..
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Is $p\mapsto \|f\|_p$ continuous?
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Must $f$ be continuous?
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Prove that $|a| < b \iff -b<a<b$
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Show f is continuous on (0, ∞) iff f is continuous at 1 for a defined function.
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Prove that the sum of two continuous functions is continuous
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Show that any bounded linear functional on a normed linear space is continuous