A selective version of the property of Reznichenko in function spaces

Pavlović, Vladimir

doi:10.1007/s10474-006-0093-x

Cited by 6 publications

(2 citation statements)

References 7 publications

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“…On the other hand the study of the close link between the properties of the closure operator of various function space topologies and certain kinds of open covers of the base space has a long history ( [12][13][14][15][16][17][18]20]). Proceeding in the spirit of these investigations we shall use the ideas presented in the proof of the previous theorem to establish the next two interesting results.…”

Section: Weak Covers and Continuous Functionsmentioning

confidence: 99%

Variations on a theorem of Arhangel’skii and Pytkeev

Pavlović

2010

Acta Math Hung

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We identify continuous real-valued functions on a Tychonoff space X with their (closed) graphs thus allowing for C(X) to naturally inherit the lower Vietoris topology from the ambient hyperspace. We then calculate a bitopological version of tightness using the weak Lindelöf numbers of finite powers of X. We also characterize bitopological versions of countable fan and strong fan tightness of the point-open topology with respect to the lower Vietoris topology on C(X) in terms of suitable covering properties of the powers X n formulated using the language of S1 and S fin selection principles.

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Section: Weak Covers and Continuous Functionsmentioning

confidence: 99%

Variations on a theorem of Arhangel’skii and Pytkeev

Pavlović

2010

Acta Math Hung

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“…Further, several weak variant of selection principles in topological spaces have appeared in the literature and studied in detail by a number of authors. Also, there are some recent papers which deals with selection principles in bitopological spaces [25,26,28,31,33,35,36]. In selection principles theory, authors study mainly in two directions : (1).…”

Section: Introductionmentioning

confidence: 99%

Selective separability in (a)topological spaces

Luthra

Chauhan

Tyagi

2021

Filomat

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In this paper, we study selective versions of separability in (a)topological spaces with the help of some strong and weak forms of open sets. For this we use the notions of semi-closure, pre-closure, ?-closure, ?-closure and ?-closure and their respective density in (a)topological spaces. The interrelationships between different types of selective versions of separability in (a)topological spaces have been given by suitable counterexamples. Sufficient conditions are given for (a)topological spaces to be (a)Rt-separable and (a)Mt-separable for each t ? {s, p, ?, ?, ?}. It is shown that under some condition (a)Mt-separability and (a)Rt-separability are equivalent.

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A selective bitopological version of the Reznichenko property in function spaces

Pavlović

2009

Topology and its Applications

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A selective version of the property of Reznichenko in function spaces

Abstract: We consider the selective version of the property of Reznichenko and find necessary and sufficient conditions under which the function space C p (X) over a Tychonoff space X satisfies this property. The dual description involves selection principles and game theory.

Cited by 6 publications

References 7 publications

Variations on a theorem of Arhangel’skii and Pytkeev

Variations on a theorem of Arhangel’skii and Pytkeev

Selective separability in (a)topological spaces

A selective bitopological version of the Reznichenko property in function spaces

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