Finite Product of Semiring of Sets

Roland Coghetto

Formalized Mathematics (2015)

  • Volume: 23, Issue: 2, page 107-114
  • ISSN: 1426-2630

Abstract

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We formalize that the image of a semiring of sets [17] by an injective function is a semiring of sets.We offer a non-trivial example of a semiring of sets in a topological space [21]. Finally, we show that the finite product of a semiring of sets is also a semiring of sets [21] and that the finite product of a classical semiring of sets [8] is a classical semiring of sets. In this case, we use here the notation from the book of Aliprantis and Border [1].

How to cite

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Roland Coghetto. "Finite Product of Semiring of Sets." Formalized Mathematics 23.2 (2015): 107-114. <http://eudml.org/doc/271763>.

@article{RolandCoghetto2015,
abstract = {We formalize that the image of a semiring of sets [17] by an injective function is a semiring of sets.We offer a non-trivial example of a semiring of sets in a topological space [21]. Finally, we show that the finite product of a semiring of sets is also a semiring of sets [21] and that the finite product of a classical semiring of sets [8] is a classical semiring of sets. In this case, we use here the notation from the book of Aliprantis and Border [1].},
author = {Roland Coghetto},
journal = {Formalized Mathematics},
keywords = {set partitions; semiring of sets},
language = {eng},
number = {2},
pages = {107-114},
title = {Finite Product of Semiring of Sets},
url = {http://eudml.org/doc/271763},
volume = {23},
year = {2015},
}

TY - JOUR
AU - Roland Coghetto
TI - Finite Product of Semiring of Sets
JO - Formalized Mathematics
PY - 2015
VL - 23
IS - 2
SP - 107
EP - 114
AB - We formalize that the image of a semiring of sets [17] by an injective function is a semiring of sets.We offer a non-trivial example of a semiring of sets in a topological space [21]. Finally, we show that the finite product of a semiring of sets is also a semiring of sets [21] and that the finite product of a classical semiring of sets [8] is a classical semiring of sets. In this case, we use here the notation from the book of Aliprantis and Border [1].
LA - eng
KW - set partitions; semiring of sets
UR - http://eudml.org/doc/271763
ER -

References

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