List questions from complete-spaces

Published on 11 Oct 2020 - 2:28

94

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$H \odot K$ complete implies $\dim H$ or $\dim K <\infty$

Published on 21 Oct 2020 - 18:20

40

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How to prove that if ${_}$ is bounded in $(C^0[0,1],‖⋅‖_∞)$, then ${_}$ is bounded in $(^0[0,1],‖⋅‖_∞)$?

Published on 26 Feb 2026 - 1:05

31

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show that the metric space = { + : , ∈ ℚ} with usual metric is incomplete

Published on 27 Oct 2020 - 0:35

75

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Complete Set-Cauchy Sequence

Published on 27 Oct 2020 - 3:23

286

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Why is the space of $L^p$ (Fourier) multipliers a Banach space? (Stein)

Published on 26 Mar 2026 - 11:18

312

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Showing a metric space is not complete by showing the set is neither open nor closed

Published on 30 Oct 2020 - 17:02

72

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Solving an equation by fixed point theorem !?

Published on 31 Oct 2020 - 15:00

1.5k

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Why natural numbers don't have supremum?

Published on 02 Nov 2020 - 12:57

52

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$(E, \| \cdot\|)$ is Banach where $E = \mathcal{C}^1([-1,1])$ and $\|f\| = \|f\|_\infty + \|f'\|_\infty$

Published on 03 Nov 2020 - 19:31

159

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Show that $\{\cos(nx)\}_{n=0}^{\infty}$ is a complete system in $L_2[0, \pi]$

Published on 13 Nov 2020 - 10:22

117

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Final step in proving $(C[0, 1], \|\cdot\|_1)$ is not a Banach space

Published on 13 Nov 2020 - 18:07

107

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Does completion of $(0,1)$ exists and does there is a metric where $[0,1]$ is not complete

Published on 19 Nov 2020 - 7:47

245

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Solve $x^3 - x - 1=0$ over $\mathbb{R} \times \mathbb{Q}_7$

Published on 20 Nov 2020 - 19:40

74

Views

Corollary: Let X be a connected and completely regular space with more than one point, then $| X | \geq | \mathbb R |$.

Published on 23 Nov 2020 - 14:07

List Question

Completeness of $L(E,F)$

$H \odot K$ complete implies $\dim H$ or $\dim K <\infty$

How to prove that if ${_}$ is bounded in $(C^0[0,1],‖⋅‖_∞)$, then ${_}$ is bounded in $(^0[0,1],‖⋅‖_∞)$?

show that the metric space = { + : , ∈ ℚ} with usual metric is incomplete

Complete Set-Cauchy Sequence

Why is the space of $L^p$ (Fourier) multipliers a Banach space? (Stein)

Showing a metric space is not complete by showing the set is neither open nor closed

Solving an equation by fixed point theorem !?

Why natural numbers don't have supremum?

$(E, \| \cdot\|)$ is Banach where $E = \mathcal{C}^1([-1,1])$ and $\|f\| = \|f\|_\infty + \|f'\|_\infty$

Show that $\{\cos(nx)\}_{n=0}^{\infty}$ is a complete system in $L_2[0, \pi]$

Final step in proving $(C[0, 1], \|\cdot\|_1)$ is not a Banach space

Does completion of $(0,1)$ exists and does there is a metric where $[0,1]$ is not complete

Solve $x^3 - x - 1=0$ over $\mathbb{R} \times \mathbb{Q}_7$

Corollary: Let X be a connected and completely regular space with more than one point, then $| X | \geq | \mathbb R |$.

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