Hostname: page-component-7bb8b95d7b-dvmhs Total loading time: 0 Render date: 2024-09-28T21:30:37.311Z Has data issue: false hasContentIssue false
  • English
  • Français

Topological separability and axioms of countability in GPO-spaces

Published online by Cambridge University Press:  17 April 2009

J.C.R. Alcantud
J.C.R. Alcantud
Affiliation:
Facultatd de Economía y Empresa, Universidad de Salamanca, E 37008 Salamanca, Spain, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we obtain characterisations of first and second countability and separability for GPO-spaces, a class of topological spaces that include LOTS and GO-spaces. Some additional results concerning the transmission of these properties to weaker/finer topologies are derived in this framework.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 1 , February 1997 , pp. 131 - 142
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Alcantud, J.C.R. and Gutiérrez, J. M., Saturated identifications and topological properties of GPO–spaces, Centre for Discrete and Applicable Mathematics Research Report Series 96, November 1995 (London School of Economics, London).Google Scholar
[2]Cech, E., Topological spaces, Academia (Czechoslovak Acadademy of Science, Praga, 1966).Google Scholar
[3]Debreu, G., ‘Representation of a preference ordering by a numerical function’, in Decision Processes, (Thrall, R.M., Coombs, C.H. and Davis, R.L., Editors) (Wiley, New York, 1954), pp. 159–165.Google Scholar
[4]Debreu, G., ‘Continuity properties of Paretian utility’, Internat. Econom. Rev. 5 (1964), 285–293.CrossRefGoogle Scholar
[5]Faber, M.J., Metrizability in generalized ordered spaces (Mathematical Centre Tracts 53, Amsterdam, 1974).Google Scholar
[6]Fishburn, P.C., Utility theory for decision making (Wiley, New York, 1970).CrossRefGoogle Scholar
[7]Heath, R.W., Lutzer, D.J. and Zenor, P.L., ‘Monotonically normal spaces’, Trans. Amer. Math. Soc. 178 (1973), 481–493.CrossRefGoogle Scholar
[8]Lutzer, D.J., ‘On generalized ordered spaces’, Dissertationes Math. 89 (1971), 1–36.Google Scholar
[9]Mehta, G., ‘Ordered topological spaces and the theorems of Debreu and Peleg’, Indian J. Pure Appl. Math. 14 (1983), 1174–1182.Google Scholar
[10]Michael, E., ‘The product of a normal space and a metric space need not be normal’, Bull. Amer. Math. Soc. 69 (1963), 375–376.CrossRefGoogle Scholar
[11]Michael, E., ‘Paracompactness and the Lindelöff property in finite and countable Cartesian products’, Compositio Math 23 (1971), 199–214.Google Scholar
[12]Wilansky, A., Topology for analysis (Robert E. Krieger Publishing Co., Malabar, Fl., 1983).Google Scholar