Geodesic
On certain localized version of uniform selection principles
Filomat, Tome 36 (2022) no. 20, p. 6855

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DOI

We intend to localize the selection principles in uniform spaces (Kočinac, 2003) by introducing their local variations, namely locally Υ-bounded spaces (where Υ is Menger, Hurewicz or Rothberger). It has been observed that the difference between uniform selection principles and the corresponding local correlatives as introduced here is reasonable enough to discuss about these new notions. Certain observations using the critical cardinals (on the uniform selection principles which have not studied before) as well as preservation like properties (on the local versions) are presented. The interrelationships between the notions considered in this paper are outlined into an implication diagram. Certain interactions between these local variations are also investigated. We present several examples to illustrate the distinguishable behaviour of the new notions.
DOI : 10.2298/FIL2220855A
Classification : 54D20, 54E15, 54E35, 54E99
Keywords: Uniform space, selection principles, M-bounded, H-bounded, R-bounded, locally M-bounded, locally H-bounded, locally R-bounded, locally precompact, locally pre-Lindelöf 
Nur Alam; Debraj Chandra. On certain localized version of uniform selection principles. Filomat, Tome 36 (2022) no. 20, p. 6855 . doi: 10.2298/FIL2220855A
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     author = {Nur Alam and Debraj Chandra},
     title = {On certain localized version of uniform selection principles},
     journal = {Filomat},
     pages = {6855 },
     year = {2022},
     volume = {36},
     number = {20},
     doi = {10.2298/FIL2220855A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2220855A/}
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