On simultaneous strong proximinality

• Autorzy: Gupta Sahil , Narang T.D.

Identyfikatory

DOI

10.21008/j.0044-4413.2021.0004

• Języki publikacji: EN

Abstrakty

EN

In this paper, we extend the notions of simultaneous strong proximinality and simultaneous strong Chebyshevity available in Banach spaces to metric spaces and prove that if W is a simultaneously approximatively compact subset of a metric space (X, d) then W is simultaneously strongly proximinal. The converse holds if the set of all best simultaneous approximations to every bounded subset S of X from W is compact. We show that simultaneously strongly Chebyshev sets are precisely the sets which are simultaneously strongly proximinal and simultaneously Chebyshev. How simultaneous strong proximinality is transmitted to and from quotient spaces has also been discussed when the underlying spaces are metric linear spaces.

Słowa kluczowe

EN

strongly proximinal; simultaneously strongly proximinal; strongly Chebyshev; simultaneously strongly Chebyshev; approximatively compact; simultaneously approximatively compact

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2021
• Tom: nr 65
• Strony: 47--55
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Gupta Sahil

• Department of Mathematics, BBK DAV College for Women, Amritsar

autor

Narang T.D.

• Department of Mathematics, Guru Nanak Dev University, Amritsar

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).