List questions from continuity

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$C(K)$ $C^*$-subalgebra of $C(K')$ if $K\subseteq K'$?

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Prove that there exist a sequence of real numbers satisfying $M_n \leq M_{n+1}$ for all $n\in \mathbb{N}$

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continues function and uniformly convergent

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Question about continuity in polar coordinate

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CDF on subset of real line is continuous if it has no atoms?

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Proof Verification: $x\sin(1/x)$ is continuous on $(0,1)$

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Show that a linear projection is continuous if it is continuous in 0

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$V$ is finite dimensional if and only if all linear operators $T\colon V \rightarrow \mathbb{K}$ are continuous.

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Is there a function with such properties?

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Any Real uniformly continuous function on bounded set is bounded

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Is a function containing a "limit" of a CDF continuous?

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Prove that $\frac{1}{\sqrt{x}}$ is continuous on $(0,\infty)$.

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Continuous functions satisfying $2f(x) = f(2x)$

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Reference for theorem bounding distances of values of uniformly continuous functions?

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List Question

Proving Uniform Continuity by Characterization of Sequences

$C(K)$ $C^*$-subalgebra of $C(K')$ if $K\subseteq K'$?

Prove that there exist a sequence of real numbers satisfying $M_n \leq M_{n+1}$ for all $n\in \mathbb{N}$

continues function and uniformly convergent

Question about continuity in polar coordinate

CDF on subset of real line is continuous if it has no atoms?

Proof Verification: $x\sin(1/x)$ is continuous on $(0,1)$

Show that a linear projection is continuous if it is continuous in 0

$V$ is finite dimensional if and only if all linear operators $T\colon V \rightarrow \mathbb{K}$ are continuous.

Is there a function with such properties?

Any Real uniformly continuous function on bounded set is bounded

Is a function containing a "limit" of a CDF continuous?

Prove that $\frac{1}{\sqrt{x}}$ is continuous on $(0,\infty)$.

Continuous functions satisfying $2f(x) = f(2x)$

Reference for theorem bounding distances of values of uniformly continuous functions?

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