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On the Linear Invariance of Lindelöf Numbers

Published online by Cambridge University Press:  20 November 2018

Jan Baars  and
Helma Gladdines
Jan Baars
Affiliation:
Faculteit der Wiskunde en Informatica, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
Helma Gladdines
Affiliation:
Faculteit der Wiskunde en Informatica, Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
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Abstract

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Let X and Y be Tychonov spaces and suppose there exists a continuous linear bijection from Cp(X)to CP(Y). In this paper we develop a method that enables us to compare the Lindelöf number of Y with the Lindelöf number of some dense subset Z of X. As a corollary we get that if for perfect spaces X and Y, CP(X) and Cp(Y)are linearly homeomorphic, then the Lindelöf numbers of Jf and Fare equal. Another result in this paper is the following. Let X and Y be any two linearly ordered perfect Tychonov spaces such that Cp(X)and Cp(Y)are linearly homeomorphic. Let be a topological property that is closed hereditary, closed under taking countable unions and closed under taking continuous images. Then X has isproperty if and only if Y has. As examples of such properties we consider certain cardinal functions.

Keywords

54C3557N17Function SpacesLindelöf Numbers
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 2 , 01 June 1996 , pp. 129 - 137
Copyright
Copyright © Canadian Mathematical Society 1996

References

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