A selective bitopological version of the Reznichenko property in function spaces

Pavlović, Vladimir

doi:10.1016/j.topol.2009.01.010

Cited by 5 publications

(3 citation statements)

References 17 publications

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“…The definition of the selective bitopological version of the Reznichenko property was given in [22]. It has been characterized by considering the compact-open and the topology of pointwise convergence on the set of all continuous real-valued functions in [23].…”

Section: Bitopological H-separability and Gn -Separabilitymentioning

confidence: 99%

Variations of selective separability and tightness in function spaces with set-open topologies

Osipov

Özçağ

2017

Topology and its Applications

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Section: Bitopological H-separability and Gn -Separabilitymentioning

confidence: 99%

Variations of selective separability and tightness in function spaces with set-open topologies

Osipov

Özçağ

2017

Topology and its Applications

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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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“…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

Cited by 5 publications

References 17 publications

Variations of selective separability and tightness in function spaces with set-open topologies

Variations of selective separability and tightness in function spaces with set-open topologies

Variations on a theorem of Arhangel’skii and Pytkeev

Selective separability in (a)topological spaces

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