List questions from general-topology

Published on 24 Mar 2026 - 15:28

411

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Definition of "Normal topological space"

Published on 25 Mar 2026 - 11:56

167

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Prove the set is not connected

Published on 22 Mar 2026 - 1:37

34

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$A$ be a basis for a topology on $X$, and $\tau_X$ be a topology on $X$ s.t $A \subseteq \tau_X$. Then can we complete $A$ to a basis of $\tau_X$?

Published on 17 Jan 2018 - 10:19

64

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Related the property of two points contained in the same component

Published on 20 Mar 2026 - 15:55

46

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Topology generated by $\mathbb{R}$-valued functions of vanishing variation

Published on 22 Mar 2026 - 7:07

268

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Family of continuous functions seperates points

Published on 17 Jan 2018 - 12:41

296

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Definitions of real projective spaces

Published on 20 Mar 2026 - 1:34

87

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Question: Is this set compact? If yes, how can I prove it?

Published on 17 Mar 2026 - 15:53

158

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Never Used Compact Closure...

Published on 20 Mar 2026 - 7:52

3.6k

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A finite topological space is T1 if and only the topology is discrete

Published on 25 Mar 2026 - 13:45

599

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Proof Verification: $1 \leq x^2 + y^2 \leq 2$ is connected?

Published on 17 Jan 2018 - 20:05

45

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Let $X$ be a topological vector space. Then how you show $A^\perp$ is closed in $X^*$ under the strong topology?

Published on 20 Mar 2026 - 10:20

119

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Sion's MinMax theorem over matrices

Published on 25 Mar 2026 - 11:54

61

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Is ${C}[0,1],\Bbb{R}$ homeomorphic to any $\Bbb{R^n}$, for an integer $n$?

Published on 22 Mar 2026 - 6:36

List Question

Forcing homeomorphism

Definition of "Normal topological space"

Prove the set is not connected

$A$ be a basis for a topology on $X$, and $\tau_X$ be a topology on $X$ s.t $A \subseteq \tau_X$. Then can we complete $A$ to a basis of $\tau_X$?

Related the property of two points contained in the same component

Topology generated by $\mathbb{R}$-valued functions of vanishing variation

Family of continuous functions seperates points

Definitions of real projective spaces

Question: Is this set compact? If yes, how can I prove it?

Never Used Compact Closure...

A finite topological space is T1 if and only the topology is discrete

Proof Verification: $1 \leq x^2 + y^2 \leq 2$ is connected?

Let $X$ be a topological vector space. Then how you show $A^\perp$ is closed in $X^*$ under the strong topology?

Sion's MinMax theorem over matrices

Is ${C}[0,1],\Bbb{R}$ homeomorphic to any $\Bbb{R^n}$, for an integer $n$?

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