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

top
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

top

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

top
  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 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.