List questions from examples-counterexamples

Published on 12 Apr 2026 - 16:28

48

Views

If $V$ is finite-dimensional and exist $\beta$ basis of $V$ such that $T(\beta)$ is a basis for $W$, then $T$ is a isomorphism?

Published on 16 Apr 2026 - 15:58

63

Views

AB does not imply KC

Published on 14 Apr 2026 - 23:58

760

Views

The product of limit point compact Hausdorff spaces is not limit point compact

Published on 10 Apr 2026 - 13:51

330

Views

Counterexample to in $\mathcal{Mod}_A$ colimits of filtered index categories are exact

Published on 16 Apr 2026 - 1:40

1.1k

Views

Explicitly showing cokernel of exponential sequence is not a sheaf

Published on 16 Apr 2026 - 8:20

239

Views

Examples of spaces in which the closure of any path connected set is path connected.

Published on 09 Apr 2026 - 0:17

1.4k

Views

State space representation of transfer function $ 1/s $

Published on 15 Apr 2026 - 15:03

375

Views

A counter example about fraction of 2 sets

Published on 13 Apr 2026 - 17:27

8.1k

Views

Proving that a ring is not a Principal Ideal Domain

Published on 11 Apr 2026 - 23:10

47.8k

Views

Injective function: example of injective function that is not surjective.

Published on 11 Apr 2026 - 7:17

541

Views

Counterexample to second derivative test when f''(x) is not continuously differentiable

Published on 10 Apr 2026 - 2:14

85

Views

Another question on second countable spaces

Published on 11 Apr 2026 - 12:51

93

Views

Counterexample to $\operatorname{Supp} \mathcal G \subset Z \hookrightarrow X$ but $\mathcal G\cong i_*i^{-1}\mathcal G$ when $Z$ is not closed

Published on 14 Apr 2026 - 16:24

114

Views

A question on spaces with calibre-$\aleph_1$

Published on 17 Apr 2026 - 3:29

List Question

Non abelian group with normal subgroup

If $V$ is finite-dimensional and exist $\beta$ basis of $V$ such that $T(\beta)$ is a basis for $W$, then $T$ is a isomorphism?

AB does not imply KC

The product of limit point compact Hausdorff spaces is not limit point compact

Counterexample to in $\mathcal{Mod}_A$ colimits of filtered index categories are exact

Explicitly showing cokernel of exponential sequence is not a sheaf

Examples of spaces in which the closure of any path connected set is path connected.

State space representation of transfer function $ 1/s $

A counter example about fraction of 2 sets

Proving that a ring is not a Principal Ideal Domain

Injective function: example of injective function that is not surjective.

Counterexample to second derivative test when f''(x) is not continuously differentiable

Another question on second countable spaces

Counterexample to $\operatorname{Supp} \mathcal G \subset Z \hookrightarrow X$ but $\mathcal G\cong i_*i^{-1}\mathcal G$ when $Z$ is not closed

A question on spaces with calibre-$\aleph_1$

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