List questions from examples-counterexamples

Published on 15 Apr 2026 - 3:25

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Prove or find a counter example to the following statements regarding limits

Published on 16 Apr 2026 - 3:35

219

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Martingale counterexample construction

Published on 10 Apr 2026 - 16:37

91

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Counter-example: A non-continuous closed surjection from a normal space onto a non-normal space

Published on 14 Apr 2026 - 15:48

263

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Injection and surjection over reals such that the composite are neither injection or surjection

Published on 16 Apr 2026 - 0:36

196

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Second Countability in Lusin's Theorem

Published on 15 Apr 2026 - 11:05

807

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Partially Ordered Set that is NOT a lattice?

Published on 13 Apr 2026 - 4:54

342

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Nonhomeomorphic subsets of the plane

Published on 15 Apr 2026 - 5:57

241

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Can the sequence of derivatives $\{f^{(k)}(0)\}_{k\geq 1}$ be any sequence?

Published on 14 Apr 2026 - 12:16

324

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Uniform integrability of continuous function of conditional expectations

Published on 11 Apr 2026 - 12:19

230

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Do homeomophisms of subspaces preserve the subspaces topological structure in the parent space?

Published on 10 Apr 2026 - 19:54

103

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Algebraic complementary spaces which are not topologically complementary

Published on 13 Apr 2026 - 21:18

343

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Which counterexamples to keep in mind when studying (Lebesgue) integral convergence theorems

Published on 09 Apr 2026 - 6:10

304

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The interior of a countable set is always empty?

Published on 14 Apr 2026 - 19:42

701

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Example of submanifold without subspace topology

Published on 28 Mar 2026 - 20:57

List Question

Counterexample to see that a formula is $F$

Prove or find a counter example to the following statements regarding limits

Martingale counterexample construction

Counter-example: A non-continuous closed surjection from a normal space onto a non-normal space

Injection and surjection over reals such that the composite are neither injection or surjection

Second Countability in Lusin's Theorem

Partially Ordered Set that is NOT a lattice?

Nonhomeomorphic subsets of the plane

Can the sequence of derivatives $\{f^{(k)}(0)\}_{k\geq 1}$ be any sequence?

Uniform integrability of continuous function of conditional expectations

Do homeomophisms of subspaces preserve the subspaces topological structure in the parent space?

Algebraic complementary spaces which are not topologically complementary

Which counterexamples to keep in mind when studying (Lebesgue) integral convergence theorems

The interior of a countable set is always empty?

Example of submanifold without subspace topology

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