List questions from continuity

Published on 18 Oct 2018 - 8:21

139

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Details in proving that the image of a dense subset of a domain is itself dense in the range

Published on 18 Oct 2018 - 8:55

2.9k

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Please clarify proof that $\mathbb R_K$ is not path connected.

Published on 29 Mar 2026 - 6:28

61

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Is there a relation between a smooth function and a separable function?

Published on 18 Oct 2018 - 15:10

276

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Continuity of supremum of polynomial

Published on 26 Mar 2026 - 6:07

43

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$\vert f'(a) \vert < k$,prove that there exists $I$, $a\in I$ that $\vert f'(x)\vert<k$, $f \in C^1$

Published on 26 Mar 2026 - 3:13

357

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Continuous map but not bounded on Banach space

Published on 25 Mar 2026 - 2:59

384

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Having trouble showing a function is continuous: $x/(1+|x|)$

Published on 26 Mar 2026 - 1:00

209

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Certain cylinder is homeomorphic to $S^1\times [1,2]$

Published on 20 Oct 2018 - 22:32

62

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Show multivariable quadratic function is continuous?

Published on 20 Oct 2018 - 23:25

76

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Proof of continuity at a point

Published on 02 Apr 2026 - 14:48

347

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Homeomorphism between annulus and $S^1\times [1,2]$

Published on 21 Oct 2018 - 1:08

85

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$X\times Y$ homeomorphic to $X^{} \times Y^{}$ Proof Verification

Published on 21 Oct 2018 - 15:30

34

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Sequentially Continuous Sequence

Published on 21 Oct 2018 - 16:03

27

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How does uniform continuity and continuity affect the convergence of a function

Published on 26 Mar 2026 - 11:16

List Question

Showing a function is discontinuous using open sets

Details in proving that the image of a dense subset of a domain is itself dense in the range

Please clarify proof that $\mathbb R_K$ is not path connected.

Is there a relation between a smooth function and a separable function?

Continuity of supremum of polynomial

$\vert f'(a) \vert < k$,prove that there exists $I$, $a\in I$ that $\vert f'(x)\vert<k$, $f \in C^1$

Continuous map but not bounded on Banach space

Having trouble showing a function is continuous: $x/(1+|x|)$

Certain cylinder is homeomorphic to $S^1\times [1,2]$

Show multivariable quadratic function is continuous?

Proof of continuity at a point

Homeomorphism between annulus and $S^1\times [1,2]$

$X\times Y$ homeomorphic to $X^{} \times Y^{}$ Proof Verification

Sequentially Continuous Sequence

How does uniform continuity and continuity affect the convergence of a function

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