On some inclusion in the set theory

• Autorzy: Ochab Justyna , Ulaszek Marcin

Identyfikatory

DOI

10.7862/rf.2022.6

• Języki publikacji: EN

Abstrakty

EN

This note contains the proof of an inclusion in the set theory. In that proof we use only basic laws appearing in the set theory. More precisely, using some basic laws of the set theory we provide the proof of an inclusion which is applied in the proof of certain theorem of the classical measure theory. The presented paper has an elementary character. Only the basic tools of the set theory are involved.

Słowa kluczowe

EN

set theory; inclusion; distributivity over union; distributivity over intersection

PL

teoria zbiorów; włączenie; dystrybutywność

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2022
• Tom: Vol. 45
• Strony: 129--132
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Ochab Justyna

• Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, al. Powstańców Warszawy 8, 35-959 Rzeszów, Poland

• https://orcid.org/0000-0001-5749-5807

autor

Ulaszek Marcin

• Faculty of Mathematics and Applied Physics, Rzeszów University of Technology, al. Powstańców Warszawy 8, 35-959 Rzeszów, Poland

• https://orcid.org/0000-0002-2624-4172

Bibliografia

• [1] J. Banaś, S. Wędrychowicz, Collection of Exercises in Mathematical Analysis, Wydawnictwo Naukowe PWN, Warsaw, 2020 (in Polish).
• [2] R. Engelking, General Topology, Wydawnictwo Naukowe PWN, Warsaw, 2007 (in Polish).
• [3] K. Kuratowski, Introduction to Set Theory and Topology, Wydawnictwo Naukowe PWN, Warsaw, 2007 (in Polish).
• [4] K. Kuratowski, A. Mostowski, Set Theory, PWN, Warsaw, 1966 (in Polish).
• [5] S. Łojasiewicz, Introduction to the Theory of Real Functions, PWN, Warsaw, 1973 (in Polish).
• [6] S. Łojasiewicz, Introduction to the Theory of Real Functions, J. Wiley & Sons, Chichester, 1988.
• [7] W. Marek, J. Onyszkiewicz, Elements of the Logic and Set Theory in Exercises, Wydawnictwo Naukowe PWN, Warsaw, 2004 (in Polish).
• [8] R. Sikorski, Real Functions, PWN, Warsaw, 1958 (in Polish).