Transportable Relations

Bourbaki, N. (1957/2004). Transportable Relations: Theory of Sets. Theory of Sets.

Type

Book

Intellectual base

Review or monograph

Year

2004 this edition · first published 1957

DOI

10.1007/978-3-642-59309-3

ISBN

9783540225256

DOI registrant

Springer Nature

Link

https://doi.org/10.1007/978-3-642-59309-3

Cited from

mathematics

Cited by

4 citations across 4 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Cartesian Product
  • Mathematics. The Cartesian plane \(\mathbb{R} \times \mathbb{R}\), product spaces and product topologies, joint sample spaces, Cartesian-closed categories, and the underlying construction of relations and functions as sets of tuples.

    This sourceFoundational set-theoretic development of the Cartesian product, ordered pairs, product sets, and relations/functions as sets of tuples.

• Indexed family
  • Its autonomous core is addressed collection structure, distinct from an unindexed set that removes repetitions, an ordered sequence restricted to natural indices, a multiset without arbitrary labels or a partial lookup with missing required indices.

Domain-specific

• Binary relation
  • A binary relation from X to Y is a subset R of the Cartesian product X×Y; x is related to y exactly when the ordered pair (x,y) belongs to R.
• Transport of Structure
  • Bourbaki made this operation explicit in its treatment of species of structures, isomorphisms, and transportable relations; universal algebra expresses the same construction through operations and identities.

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