New soft separation axioms and fixed soft points with respect to total belong and total non-belong relations

• Autorzy: Al-shami Tareq M. , Tercan Adnan , Mhemdi Abdelwaheb

Identyfikatory

DOI

10.1515/dema-2021-0018

• Języki publikacji: EN

Abstrakty

EN

In this article, we exploit the relations of total belong and total non-belong to introduce new soft separation axioms with respect to ordinary points, namely tt-soft pre Ti (i = 0, 1, 2, 3, 4) and tt-soft pre-regular spaces. The motivations to use these relations are, first, cancel the constant shape of soft pre-open and pre-closed subsets of soft pre-regular spaces, and second, generalization of existing comparable properties on classical topology. With the help of examples, we show the relationships between them as well as with soft pre Ti (i = 0, 1, 2, 3, 4) and soft pre-regular spaces. Also, we explain the role of soft hyperconnected and extended soft topological spaces in obtaining some interesting results. We characterize a tt-soft pre-regular space and demonstrate that it guarantees the equivalence of tt-soft pre Ti (i = 0, 1, 2). Furthermore, we investigate the behaviors of these soft separation axioms with the concepts of productand sum of soft spaces. Finally, we introduce a concept of pre-fixed soft point and study its main properties.

Słowa kluczowe

EN

soft pre-open set; tt-soft preTi-space; extended soft topology; soft hyperconnected space; additive property; topological property; soft pre-compact space; pre-fixed soft point

PL

zbiór pre-otwarty; zbiór otwarty; miękki zbiór otwarty; przestrzenie topologiczne; właściwość addytywna; przestrzeń zwarta; punkt stały

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2021
• Tom: Vol. 54, nr 1
• Strony: 196--211
• Opis fizyczny: Bibliogr. 33 poz.

Twórcy

autor

Al-shami Tareq M.

• Department of Mathematics, Sana’a University, Sana’a, Yemen

autor

Tercan Adnan

• Department of Mathematics, Hacettepe University, Ankara, Turkey

autor

Mhemdi Abdelwaheb

• Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz University, Riyadh, Saudi Arabia

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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).