Function spaces and a property of Reznichenko

Ljubiša D. Kočinac; Marion Scheepers

doi:10.1016/S0166-8641(01)00177-8

Function spaces and a property of Reznichenko

Ljubiša D. Kočinac
, Marion Scheepers

Mathematics Department

University of Nis

Research output: Contribution to journal › Article › peer-review

36 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	135-143
Number of pages	9
Journal	Topology and its Applications
Volume	123
Issue number	1
DOIs	https://doi.org/10.1016/S0166-8641(01)00177-8
State	Published - 31 Aug 2002

Keywords

Countable strong fan tightness
Hurewicz property
Property (*)
Reznichenko property
Rothberger property
ω-cover
ω-grouping property

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title = "Function spaces and a property of Reznichenko",

abstract = "In this paper we show that for a set X of real numbers the function space Cp(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.",

keywords = "Countable strong fan tightness, Hurewicz property, Property (*), Reznichenko property, Rothberger property, ω-cover, ω-grouping property",

author = "Ko{\v c}inac, \{Ljubi{\v s}a D.\} and Marion Scheepers",

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doi = "10.1016/S0166-8641(01)00177-8",

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TY - JOUR

T1 - Function spaces and a property of Reznichenko

AU - Kočinac, Ljubiša D.

AU - Scheepers, Marion

PY - 2002/8/31

Y1 - 2002/8/31

N2 - In this paper we show that for a set X of real numbers the function space Cp(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.

AB - In this paper we show that for a set X of real numbers the function space Cp(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.

KW - Countable strong fan tightness

KW - Hurewicz property

KW - Property ()

KW - Reznichenko property

KW - Rothberger property

KW - ω-cover

KW - ω-grouping property

UR - https://www.scopus.com/pages/publications/0038351837

U2 - 10.1016/S0166-8641(01)00177-8

DO - 10.1016/S0166-8641(01)00177-8

M3 - Article

AN - SCOPUS:0038351837

SN - 0166-8641

VL - 123

SP - 135

EP - 143

JO - Topology and its Applications

JF - Topology and its Applications

IS - 1

ER -

Function spaces and a property of Reznichenko

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Keywords

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