List questions from equivalence-relations

52

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Show that $(a, x) \sim (b, y) \iff w(ay - bx) = 0, \text{ for some } w \in S$ defines an equivalence relation on $R \times S$.

Published on 31 Mar 2026 - 13:15

89

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Tammo tom Dieck's definition of Clutching

Published on 10 Aug 2020 - 20:15

296

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If $S$ and $R$ are equivalence relations on $A$, and $A/R=A/S$, then $R=S$

Published on 11 Aug 2020 - 19:01

1k

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The role of Injectivity and Surjectivity on Equivalence Classes

Published on 08 Apr 2026 - 23:04

109

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Example of a minimal equivalence relation on $A$ containing $R$

Published on 12 Aug 2020 - 23:39

60

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Is there always a labeling function for any equivalence relations?

Published on 08 Apr 2026 - 19:09

48

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Equivalence Class of Empty Set

Published on 13 Aug 2020 - 2:46

98

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Finding the minimal equivalence relation containing each of the relations given

Published on 13 Aug 2020 - 9:56

39

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Operation on the group is well defined "in the first and second factor".

Published on 28 Mar 2026 - 0:00

407

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(X subset of Y or Y subset of X) is transitive?

Published on 15 Aug 2020 - 13:01

186

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More natural ways to view things that are usually described as equivalence classes

Published on 21 Aug 2020 - 12:26

214

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How do I prove that the typical fibre of the associated bundle $(P_F:=(P\times F)/\sim_G,\pi_F,M)$ is $F$?

Published on 27 Mar 2026 - 19:54

307

Views

Is the metric well-defined?

Published on 25 Aug 2020 - 16:52

107

Views

Why we want a function to be well-defined?

Published on 25 Aug 2020 - 20:47

88

Views

Describe the identification space $\mathbb{R}^2 / \sim $

Published on 03 Apr 2026 - 15:10

List Question

Show that $(a, x) \sim (b, y) \iff w(ay - bx) = 0, \text{ for some } w \in S$ defines an equivalence relation on $R \times S$.

Tammo tom Dieck's definition of Clutching

If $S$ and $R$ are equivalence relations on $A$, and $A/R=A/S$, then $R=S$

The role of Injectivity and Surjectivity on Equivalence Classes

Example of a minimal equivalence relation on $A$ containing $R$

Is there always a labeling function for any equivalence relations?

Equivalence Class of Empty Set

Finding the minimal equivalence relation containing each of the relations given

Operation on the group is well defined "in the first and second factor".

(X subset of Y or Y subset of X) is transitive?

More natural ways to view things that are usually described as equivalence classes

How do I prove that the typical fibre of the associated bundle $(P_F:=(P\times F)/\sim_G,\pi_F,M)$ is $F$?

Is the metric well-defined?

Why we want a function to be well-defined?

Describe the identification space $\mathbb{R}^2 / \sim $

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