A characterization of complete Boolean algebras

• Autorzy: Kubiś, W.
• Języki publikacji: EN

Abstrakty

EN

Every lattice and, in particular, every Boolean algebra is a convexity space with a naturally defined convexity structure. We characterize complete Boolean algebras as the only S3 convexity spaces having an extension property for certain classes of convexity preserving maps. This answers our question posed in [1]. Our characterization provides also a short proof of Sikorski's extension theorem for homomorphisms of Boolean algebras.

Słowa kluczowe

PL

pełna algebra Boole'a; przestrzeń wypukła

EN

complete Boolean algebra; convexity space; cp map

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2001
• Tom: Vol. 49, no 1
• Strony: 91--95
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Kubiś, W.

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland,

Bibliografia

• [1] W. Kubiś, Extension theorems in axiomatic theory of convexity, Bull. Pol. Ac.: Math., 48 (2000) 89-96.
• [2] R. Sikorski, Boolean algebras, Springer-Verlag 1960.
• [3] V. P. Soltan, An introduction to the axiomatic theory of convexity (in Russian), Shtiintsa, Kishinev 1984.
• [4] W. Szmielew, Oriented and nonoriented linear orders, Bull. Pol. Ac.: Math., 25 (1977) 659-665.
• [5] J. C. Varlet, Remarks on distributive lattices, Bull. Pol. Ac.: Math., 23 (1975) 1143-1147.
• [6] M. van de Vel, Binary convexities and distributive lattices, Proc. London Math. Soc. (3), 48 (1984) 1-33.
• [7] M. van de Vel, Theory of convex structures, North-Holland, Amsterdam 1993.