κ-compactness, extent and the Lindelöf number in LOTS

David Buhagiar; Emmanuel Chetcuti; Hans Weber

Open Mathematics (2014)

  • Volume: 12, Issue: 8, page 1249-1264
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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David Buhagiar, Emmanuel Chetcuti, and Hans Weber. "κ-compactness, extent and the Lindelöf number in LOTS." Open Mathematics 12.8 (2014): 1249-1264. <http://eudml.org/doc/269564>.

@article{DavidBuhagiar2014,
abstract = {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.},
author = {David Buhagiar, Emmanuel Chetcuti, Hans Weber},
journal = {Open Mathematics},
keywords = {Linearly ordered topological space; Lexicographic product; Generalized ordered space; ℵ-compact space; Extent; Lindelöf number; linearly ordered topological space; lexicographic product; generalized ordered space; -compact space; extent},
language = {eng},
number = {8},
pages = {1249-1264},
title = {κ-compactness, extent and the Lindelöf number in LOTS},
url = {http://eudml.org/doc/269564},
volume = {12},
year = {2014},
}

TY - JOUR
AU - David Buhagiar
AU - Emmanuel Chetcuti
AU - Hans Weber
TI - κ-compactness, extent and the Lindelöf number in LOTS
JO - Open Mathematics
PY - 2014
VL - 12
IS - 8
SP - 1249
EP - 1264
AB - 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.
LA - eng
KW - Linearly ordered topological space; Lexicographic product; Generalized ordered space; ℵ-compact space; Extent; Lindelöf number; linearly ordered topological space; lexicographic product; generalized ordered space; -compact space; extent
UR - http://eudml.org/doc/269564
ER -

References

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  1. [1] Birkhoff G., Lattice Theory, 3rd ed., Amer. Math. Soc. Colloq. Publ., 25, American Mathematical Society, Providence, 1995 
  2. [2] Buhagiar D., Miwa T., On superparacompact and Lindelöf GO-spaces, Houston J. Math., 1998, 24(3), 443–457 Zbl0977.54019
  3. [3] Faber M.J., Metrizability in Generalized Ordered Spaces, Math. Centre Tracts, 53, Mathematisch Centrum, Amsterdam, 1974 Zbl0282.54017
  4. [4] Lutzer D., On Generalized Ordered Spaces, Dissertationes Math. (Rozprawy Mat.), 89, Polish Academy of Sciences, Warsaw, 1971 
  5. [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 Zbl0808.54022
  6. [6] Nagata J., Modern General Topology, 2nd ed., North-Holland Math. Library, 33, North-Holland, Amsterdam, 1985 Zbl0598.54001
  7. [7] Stephenson R.M. Jr., Initially κ-compact and related spaces, In: Handbook of Set-Theoretic Topology, North-Holland, 1984, 603–632 

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