Two types of separation axioms on supra soft topological spaces

• Autorzy: Al-shami Tareq M. , El-Shafei Mohammed E.

Identyfikatory

DOI

10.1515/dema-2019-0016

• Języki publikacji: EN

Abstrakty

EN

In 2011, Shabir and Naz [1] employed the notion of soft sets to introduce the concept of soft topologies; and in 2014, El-Sheikh and Abd El-Latif [2] relaxed the conditions of soft topologies to construct a wider and more general class, namely supra soft topologies. In this disquisition, we continue studying supra soft topologies by presenting two kinds of supra soft separation axioms, namely supra soft Ti-spaces and supra p-soft Ti-spaces for i= 0,1,2,3,4. These two types are formulated with respect to the ordinary points; and the difference between them is attributed to the applied non belong relations in their definitions. We investigate the relationships between them and their parametric supra topologies; and we provide many examples to separately elucidate the relationships among spaces of each type. Then we elaborate that supra p-soft Ti-spaces are finer than supra soft Ti-spaces in the case of i= 0,1,4; and we demonstrate that supra soft T3-spaces are finer than supra p-soft T3-spaces. We point out that supra p-softTi-axioms imply supra p-softTi−1, however, this characterization does not hold for supra soft Ti-axioms (see, Remark (3.30)). Also, we give a complete description of the concepts of supra p-soft Ti-spaces (i= 1,2) and supra p-soft regular spaces. Moreover, we define the finite product of supra soft spaces and manifest that the finite product of supra soft Ti (supra p-soft Ti) is supra soft Ti (supra p-soft Ti) for i= 0,1,2,3. After investigating some properties of these axioms in relation with some of the supra soft topological notions such as supra soft subspaces and enriched supra soft topologies, we explore the images of these axioms under soft S*-continuous mappings. Ultimately, we provide an illustrative diagram to show the interrelations between the initiated supra soft spaces.

Słowa kluczowe

EN

supra soft Ti-space; supra p-soft Ti-space; supra soft subspace; product supra soft spaces; supra soft topological space

PL

przestrzeń topologiczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2019
• Tom: Vol. 52, nr 1
• Strony: 147--165
• Opis fizyczny: Bibliogr. 40 poz., rys.

Twórcy

autor

Al-shami Tareq M.

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

autor

El-Shafei Mohammed E.

• Department of Mathematics, Mansoura University, Mansoura, Egypt

Bibliografia

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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).