Geodesic
On the Linear Invariance of Lindelöf Numbers
Canadian mathematical bulletin, Tome 39 (1996) no. 2, pp. 129-137

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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.
DOI : 10.4153/CMB-1996-017-0
Mots-clés : 54C35, 57N17, Function Spaces, Lindelöf Numbers 
Baars, Jan; Gladdines, Helma. On the Linear Invariance of Lindelöf Numbers. Canadian mathematical bulletin, Tome 39 (1996) no. 2, pp. 129-137. doi: 10.4153/CMB-1996-017-0
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     title = {On the {Linear} {Invariance} of {Lindel\"of} {Numbers}},
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     year = {1996},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1996-017-0/}
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