List questions from examples-counterexamples

Published on 15 Apr 2026 - 4:51

590

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Example of non-separable subspace of a separable Hausdorff space

Published on 15 Apr 2026 - 6:09

60

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Proof regarding limits

Published on 08 Apr 2026 - 17:29

38

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Give an example to show that if T is the product topology on X , then $\prod_{B}$ is need not be closed( Wayne patty 2.3.8)

Published on 16 Apr 2026 - 12:28

213

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Prove that the transformation T over a unit vector is also a unit vector

Published on 14 Apr 2026 - 6:39

82

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Examples of Not Uniformly Continuous Function

Published on 12 Apr 2026 - 1:48

625

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Countexample: Sum and Product of two non-zero nilpotent operators is nilpotent?

Published on 17 Apr 2026 - 2:40

201

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Does there exist a $4\times4$ matrix $A$ such that $A$ and $A^2$ are not normal but $A^3$ is normal?

Published on 12 Apr 2026 - 5:14

104

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Counterexample: There exist non-zero nilpotent matrices $A$ and $B$ that $AB$ is non-negative

Published on 15 Apr 2026 - 7:52

44

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I need a concrete example to show this equality is false

Published on 13 Apr 2026 - 0:14

183

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Counter example in Sobolev space

Published on 11 Apr 2026 - 8:10

614

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Continuous if and only if graph of every path connected subspace is path connected?

Published on 13 Apr 2026 - 8:32

816

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If $E(X_n) \to E(X)$, does this imply convergence in $L^1$?

Published on 15 Apr 2026 - 18:47

84

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Finding example of a compact metric space a non hausdorff Topological space and a continuous function that maps X onto Y

Published on 14 Apr 2026 - 0:34

77

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Converse of density theorem for $L^1(\Omega)$

Published on 09 Apr 2026 - 9:10

List Question

Proving or disproving a claim about limits

Example of non-separable subspace of a separable Hausdorff space

Proof regarding limits

Give an example to show that if T is the product topology on X , then $\prod_{B}$ is need not be closed( Wayne patty 2.3.8)

Prove that the transformation T over a unit vector is also a unit vector

Examples of Not Uniformly Continuous Function

Countexample: Sum and Product of two non-zero nilpotent operators is nilpotent?

Does there exist a $4\times4$ matrix $A$ such that $A$ and $A^2$ are not normal but $A^3$ is normal?

Counterexample: There exist non-zero nilpotent matrices $A$ and $B$ that $AB$ is non-negative

I need a concrete example to show this equality is false

Counter example in Sobolev space

Continuous if and only if graph of every path connected subspace is path connected?

If $E(X_n) \to E(X)$, does this imply convergence in $L^1$?

Finding example of a compact metric space a non hausdorff Topological space and a continuous function that maps X onto Y

Converse of density theorem for $L^1(\Omega)$

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