κ-compactness, extent and the Lindelöf number in LOTS

• Autorzy: David Buhagiar , Emmanuel Chetcuti , Hans Weber
• Języki publikacji: EN

Abstrakty

EN

We study the behaviour of ℵ-compactness, extent and Lindelöf number in lexicographic products of linearly ordered spaces. It is seen, in particular, that for the case that all spaces are bounded all these properties behave very well when taking lexicographic products. We also give characterizations of these notions for generalized ordered spaces.

Słowa kluczowe

EN

Linearly ordered topological space; Lexicographic product; Generalized ordered space; ℵ-compact space; Extent; Lindelöf number

Kategorie tematyczne

• 06F30: Topological lattices, order topologies
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
• 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 8
• Strony: 1249-1264

Daty

wydano

2014-08-01

online

2014-05-08

Twórcy

autor

David Buhagiar

• University of Malta

autor

Emmanuel Chetcuti

• University of Malta

autor

Hans Weber

• Università degli Studi di Udine

Bibliografia

• [1] Birkhoff G., Lattice Theory, 3rd ed., Amer. Math. Soc. Colloq. Publ., 25, American Mathematical Society, Providence, 1995
• [2] Buhagiar D., Miwa T., On superparacompact and Lindelöf GO-spaces, Houston J. Math., 1998, 24(3), 443–457
• [3] Faber M.J., Metrizability in Generalized Ordered Spaces, Math. Centre Tracts, 53, Mathematisch Centrum, Amsterdam, 1974
• [4] Lutzer D., On Generalized Ordered Spaces, Dissertationes Math. (Rozprawy Mat.), 89, Polish Academy of Sciences, Warsaw, 1971
• [5] Miwa T., Kemoto N., Linearly ordered extensions of GO-spaces, Topology Appl., 1993, 54(1–3), 133–140 http://dx.doi.org/10.1016/0166-8641(93)90057-K
• [6] Nagata J., Modern General Topology, 2nd ed., North-Holland Math. Library, 33, North-Holland, Amsterdam, 1985
• [7] Stephenson R.M. Jr., Initially κ-compact and related spaces, In: Handbook of Set-Theoretic Topology, North-Holland, 1984, 603–632

Identyfikatory

DOI

10.2478/s11533-014-0407-0