Finite Product of Semiring of Sets

• Autorzy: Roland Coghetto
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

set partitions; semiring of sets

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2015
• Tom: 23
• Numer: 2
• Strony: 107-114

Daty

wydano

2015-06-01

otrzymano

2015-04-19

online

2015-08-13

Twórcy

autor

Roland Coghetto

• Rue de la Brasserie 5 7100 La Louvière, Belgium

Bibliografia

• [1] Charalambos D. Aliprantis and Kim C. Border. Infinite dimensional analysis. Springer- Verlag, Berlin, Heidelberg, 2006.
• [2] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
• [3] Grzegorz Bancerek. König’s theorem. Formalized Mathematics, 1(3):589-593, 1990.
• [4] Grzegorz Bancerek. Tarski’s classes and ranks. Formalized Mathematics, 1(3):563-567, 1990.
• [5] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
• [6] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
• [7] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
• [8] Vladimir Igorevich Bogachev and Maria Aparecida Soares Ruas. Measure theory, volume 1. Springer, 2007.
• [9] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
• [10] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
• [11] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
• [12] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
• [13] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
• [14] Roland Coghetto. Semiring of sets. Formalized Mathematics, 22(1):79-84, 2014. doi:10.2478/forma-2014-0008.
• [15] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
• [16] Noboru Endou, Kazuhisa Nakasho, and Yasunari Shidama. σ-ring and σ-algebra of sets. Formalized Mathematics, 23(1):51-57, 2015. doi:10.2478/forma-2015-0004.
• [17] D.F. Goguadze. About the notion of semiring of sets. Mathematical Notes, 74:346-351, 2003. ISSN 0001-4346. doi:10.1023/A:1026102701631.
• [18] Zbigniew Karno. On discrete and almost discrete topological spaces. Formalized Mathematics, 3(2):305-310, 1992.
• [19] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
• [20] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
• [21] Jean Schmets. Théorie de la mesure. Notes de cours, Université de Liège, 146 pages, 2004.
• [22] Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25-34, 1990.
• [23] Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1 (1):187-190, 1990.
• [24] Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 1990.
• [25] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
• [26] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
• [27] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

Identyfikatory

DOI

10.1515/forma-2015-0011