List questions from examples-counterexamples

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How common is it for a densely-defined linear functional to be closed?

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Rank of free submodules of a free module over a commutative ring.

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Counterexample to a lemma about modules

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How to define a surface which includes three coordinate axes?

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Normal products of groups with maximal nilpotency class

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seek a special matrix

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How $|\mathbb R|$ is not weakly compact

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Are compact spaces characterized by "closed maps to Hausdorff spaces"?

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T4 and first countable topology that is non metrizable

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supple, non flabby sheaf

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Does There exist a continuous bijection $\mathbb{Q}\to \mathbb{Q}\times \mathbb{Q}$?

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Example of an integrable function with an entire extension and whose derivative only vanishes at infinity

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Example of a set $Y$ that has zero Lebesgue measure and a continuous function $f$ such that $f(Y)$ is not a set of zero Lebesgue measure.

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Seeking counterexample or proof for equivalence of two separation properties

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List Question

Counterexamples to particular questions in group theory

How common is it for a densely-defined linear functional to be closed?

Rank of free submodules of a free module over a commutative ring.

Counterexample to a lemma about modules

How to define a surface which includes three coordinate axes?

Normal products of groups with maximal nilpotency class

seek a special matrix

How $|\mathbb R|$ is not weakly compact

Are compact spaces characterized by "closed maps to Hausdorff spaces"?

T4 and first countable topology that is non metrizable

supple, non flabby sheaf

Does There exist a continuous bijection $\mathbb{Q}\to \mathbb{Q}\times \mathbb{Q}$?

Example of an integrable function with an entire extension and whose derivative only vanishes at infinity

Example of a set $Y$ that has zero Lebesgue measure and a continuous function $f$ such that $f(Y)$ is not a set of zero Lebesgue measure.

Seeking counterexample or proof for equivalence of two separation properties

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