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File: Bijection.png ( 32.95 KB , 1200x1200 , 1664017449826.png )

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  No. 310
>>600 >>406 >>409 >>410
>Bijection
>Isomorphism
>Equivalence Relation
It's all just the same, innit?
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  No. 361
Isomorphisms are more than just bijections, they usually preserve some operation too.
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  No. 364 >>435
"Bijection" and "Isomorphism" are similar, but "Equivalence Relation" is different.
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  No. 406 >>409
>>310
For example, a isomorphism between groups is a bijection between the underlying sets such that the unit, inverse and multiplication are preserved.
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  No. 408
>is a relation between 2 sets
>is about structures as I remember. Don't care.
>Is about true value.

They are similar concepts, as I know.
The last thing is relevant for IIF.
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  No. 409
>>310
>>406
Yup. Isomorphism is a bijection that preserves any structure we care about. For groups, it's the group structure, homeomorphisms preserve the continuity both ways, diffeomorphisms preserve both the continuity and the differentiability. Thus we would say "the notion of isomorphism for a structure" is diffeo/homeo/etc/morphism.
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  No. 410
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  No. 435
>>364
An isomorphism induces an equivalence between one structure with another. You can even give it a equality meaning using univalence axiom.
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  No. 553
equivalence relation is different
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  No. 600
>>310
functions are set homomorphisms
bijections are set isomorphisms

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