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Function spaces and a property of Reznichenko☆☆The work for this paper was done while Scheepers was visiting Kočinac during May/June 1998 at the Department of Mathematics in the Faculty of Philosophy of the University of Niš, Yugoslavia. by Ljubiša D. Kočinac; Marion Scheepers is a Mathematics article available to read on EtoBox.

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In this paper we show that for a set X of real numbers the function space C p (X) has both a property introduced by Sakai in [Proc. Amer. Math. Soc. 104 (1988) 917-919] and a property introduced by Reznichenko (see [Topology Appl. 104 (2000) 181-190]) if and only if all finite powers of X have a property that was introduced by Gerlits and Nagy in [Topology Appl. 14 (1982) 151-161]. It follows that the minimal cardinality of a set of real numbers for which the function space does not have the properties of Sakai and Reznichenko is equal to the additivity of the ideal of first category sets of real numbers.

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Author

Ljubiša D. Kočinac; Marion Scheepers

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0166-8641)

Published

2002

Language

EN

Field

Mathematics (Physical Sciences)