Menger and Menger-type star selection principles for hit-and-miss topology

Cruz-Castillo, Ricardo; Ramírez-Páramo, Alejandro; Tenorio, Jesús F.

doi:10.1016/j.topol.2020.107574

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Some Observations On Pixley-roy Hyperspaces1

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Cited by 11 publications

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“…The first study of star-Mengerness in Pixley-Roy spaces was appeared in [18] (see also [25]). For recent developments of the study of star selection principles in hyperspaces, see [10]. We begin with an illustrative example (Proposition 3.9) of a Pixley-Roy space which is locally star-Menger without being star-Menger.…”

Section: Some Observations On Pixley-roy Hyperspacesmentioning

confidence: 99%

On localization of the star-Menger selection principle

Chandra

Alam

2021

Hacettepe Journal of Mathematics and Statistics

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In this paper we primarily introduce the local version of star-Menger property, namely locally star-Menger property (a space with this property is called locally star-Menger) and present some important topological observations. Certain interactions between the new notion and star-Menger property are also observed. Some observations on effectively locally star-Menger Pixley-Roy hyperspaces (introduced here) are obtained. Preservation like properties under several topological operations are also interpreted carefully. Besides, several results on decomposition and remainder of locally star-Menger spaces are also presented.

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Section: Some Observations On Pixley-roy Hyperspacesmentioning

confidence: 99%