Asia Mathematika

An International Journal. ISSN: 2457-0834 (online)

Volume 2, Issue 2, August 2018, Pages: 41-48

Semi-Compact and Semi-Lindelӧf Spaces via Neutrosophic Crisp Set Theory

A.A. Salama, I.M.Hanafy and M. S. Dabash

Department of Mathematics and Computer Science, Faculty of Sciences, Port Said University, Egypt.


The aim of this paper is devoted to introduce and study the concepts of semi-compact (resp. semi-Lindelӧf, locally semi-compact) spaces in a neutrosophic crisp topological space. Several properties, functions properties of neutrosophic crisp semi-compact spaces are studied. In addition to these, we introduce and study the definition of neutrosophic crisp semi-Lindelӧf spaces and neutrosophic crisp locally semi-compact spaces. We show that neutrosophic crisp semi-compact spaces is preserved under neutrosophic crisp irresolute function and neutrosophic crisp pre-semi-closed function with neutrosophic crisp semi-compact point inverses.


Neutrosophic crisp semi-compact spaces, Neutrosophic crisp semi-Lindelӧf spaces, Neutrosophic crisp locally semi-compact spaces. Neutrosophic topological spaces



1 M. C. Cueva and J. Dontchev, “On spaces with hereditarily compact α-topologies,” ActaMathematicaHungarica, vol. 82, no. 1-2, pp. 121–129, 1999.

2 J. Dontchev and M. Ganster, “On covering spaces with semi-regular sets,” Ricerche di Matematica, vol. 45, no. 1, pp. 229–245, 1996.

3 C. Dorsett, “Semi-compactness, semiseparation axioms, and product spaces,” Bulletin of the Malaysian Mathematical Sciences Soceity, vol. 4, no. 1, pp. 21–28, 1981.

4 M. Ganster, “On covering properties and generalized open sets in topological spaces,” Mathematical Chronicle, vol. 19, pp. 27–33, 1990.

5 I.M.Hanafy, A.A.Salama, Hewayda ElGhawalby and M.S.Dabash, "Some GIS Topological Concepts via Neutrosophic Crisp Set Theory", To be published in the book titled "New Trends in Neutrosophic Theories and Applications", Publisher: Europa Nova, Brussels, 2016.

6 I. L. Reilly and M. K. Vamanamurthy, “On α-continuity in topological spaces, ”Acta Mathematica Hungarica", vol. 45, no. 1-2, pp. 27–32, 1985.

7 A.A.Salama, "Fuzzy Hausdorff spaces and fuzzy irresolute functions via fuzzy ideals", V Italian-Spanish Conference on General Topology and its Applications June 21-23, 2004 Almeria, Spain.

8 A.A.Salama, F. Smarandache and ValeriKroumov. "Neutrosophic crisp Sets & Neutrosophic crisp Topological Spaces", Neutrosophic Sets and System, Vol. (2), (2014), 25-30

9 A.A.Salama and Florentin Smarandache,"Neutrosophic crisp set theory", Educational Publisher, Columbus, (2015).USA.

10 Mohammad S. Sarsak, "On Semi-compact Set and Associated Properties", International Journal of Mathematics and mathematical sciences, vol. 3, pp. 8, (2009).

11 A. A. Salama, F. Smarandache, S. A Alblowi, New neutrosophic crisp topological concepts, Neutrosophic Sets and Systems 2 (2014) 50 – 54.

12 A. A. Salama, Hewayda ElGhawalby, Asmaa.M.Nasr, Retract Neutrosophic Crisp System for Gray Scale Image, Asian Journal of Mathematics and Computer Research, ISSN No. : 2395-4205 (Print), 2395-4213 (Online), Vol.: 24, Issue.: 3, pp104-117

13 Eman.M.El-Nakeeb, Hewayda ElGhawalby, A. A. Salama, S.A. El-Hafeez. (2017). Neutrosophic Crisp Mathematical Morphology, Neutrosophic Sets and Systems, Vol. 16, 57- 69.

14 A.A. Salama, Hewayda, ElGhawalby and Shimaa Fathi Ali. (2017). Topological Manifold Space via Neutrosophic Crisp Set Theory, Neutrosophic Sets and Systems, Vol.15, 18-21.

15 A. A. Salama, I. M. Hanafy, Hewayda Elghawalby, M. S. Dabash. (2016). Neutrosophic Crisp α-Topological Spaces, Neutrosophic Sets and Systems, vol. 12, 92-96.

16 A. A. Salama, Said Broumi and Florentin Smarandache. (2014). Introduction to Neutrosophic Topological Spatial Region, Possible Application to GIS Topological Rules. I.J. Information Engineering and Electronic Business, 6, pp15-21.

17 A. A. Salama. (2013). Neutrosophic Crisp Points & Neutrosophic Crisp Ideals, Neutrosophic Sets and Systems, Vol. 1, 50-53.

18 A. A. Salama, Florentin Smarandache. (2013). Filters via Neutrosophic Crisp Sets, Neutrosophic Sets and Systems, vol. 1, 34-37.

19 A.A. Salama, S.A. Alblowi. (2012). Generalized neutrosophic set and generalized neutrosophic topological spaces.Computer Science and Engineering. 2, 129-132.

20 A.A. Salama and S.A. Alblowi. (2012). Neutrosophic Set and Neutrosophic Topological Space, ISOR J. mathematics (IOSR-JM), 3 (4), 31-35.

21 A. A. Salama. (2015). Basic Structure of Some Classes of Neutrosophic Crisp Nearly Open Sets & Possible Application to GIS Topology, Neutrosophic Sets and Systems, vol. 7, pp. 18-22.

Visitors count

Join us