List questions from quotient-spaces

Published on 16 Apr 2026 - 5:41

362

Views

Are $\mathbb{R}[X] / (X^2 +1)$ and $\mathbb{C}$ homeomorphic?

Published on 13 Apr 2026 - 20:59

109

Views

Why do we not have any subgroup of ${\mathbb Z}/{4 \mathbb Z}$ which maps isomorphically to the quotient group?

Published on 10 May 2026 - 16:06

238

Views

Equivalence relation closed in product, but not closed?

Published on 11 Apr 2026 - 0:03

2.2k

Views

Real projective space is Hausdorff: is this proof correct?

Published on 16 Apr 2026 - 10:11

349

Views

Composition of an Affine Map and the Quotient Map is Injective

Published on 12 Apr 2026 - 20:22

44

Views

Identification Space in the plane

Published on 10 May 2026 - 12:31

821

Views

How do we define functions on quotient sets?

Published on 10 May 2026 - 19:21

116

Views

Isomorphism theorem like theorem for cosets

Published on 11 May 2026 - 2:39

81

Views

If $A= \mathbb{Z}[X]/(X^n+1)$, is it true that $A/mA \cong \mathbb{Z}_m[X]/(X^n+1)$?

Published on 10 May 2026 - 17:16

1.1k

Views

Show that $\mathbb{R}^2/∼$ is homeomorphic to $\mathbb{R}$

Published on 25 Mar 2026 - 8:13

232

Views

Homogeneous space and nice manifolds

Published on 10 May 2026 - 14:04

443

Views

Homogeneous space and quotient space for complex projective spaces

Published on 10 May 2026 - 14:04

691

Views

Quotient of $[-1,1]$ homeomorphic to unit circle

Published on 12 Apr 2026 - 12:40

198

Views

Homogeneous space and quotient space for real projective spaces

Published on 10 May 2026 - 14:05

List Question

Prove that the Kolmogorov Quotient is $T_0$

Are $\mathbb{R}[X] / (X^2 +1)$ and $\mathbb{C}$ homeomorphic?

Why do we not have any subgroup of ${\mathbb Z}/{4 \mathbb Z}$ which maps isomorphically to the quotient group?

Equivalence relation closed in product, but not closed?

Real projective space is Hausdorff: is this proof correct?

Composition of an Affine Map and the Quotient Map is Injective

Identification Space in the plane

How do we define functions on quotient sets?

Isomorphism theorem like theorem for cosets

If $A= \mathbb{Z}[X]/(X^n+1)$, is it true that $A/mA \cong \mathbb{Z}_m[X]/(X^n+1)$?

Show that $\mathbb{R}^2/∼$ is homeomorphic to $\mathbb{R}$

Homogeneous space and nice manifolds

Homogeneous space and quotient space for complex projective spaces

Quotient of $[-1,1]$ homeomorphic to unit circle

Homogeneous space and quotient space for real projective spaces

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