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Int. J. Fuzzy Log. Intell. Syst. 2010; 10(4): 296-302

Published online December 1, 2010

© The Korean Institute of Intelligent Systems

## On Fuzzifying Nearly Compact Spaces

A.M. Zahran,O.R. Sayed,M. Azab Abd-Allah,A.K. Mousa

### Abstract

This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies) introduced by Ying [16, (I)]. It investigates topological notions defined by means of regular open sets when these are planted into the framework of Ying's fuzzifying topological spaces (in Łukasiewwicz fuzzy logic). The concept of fuzzifying nearly compact spaces is introduced and some of its properties are obtained. We use the finite intersection property to give a characterization of fuzzifying nearly compact spaces. Furthermore, we study the image of fuzzifying nearly compact spaces under fuzzifying completely continuous functions, fuzzifying almost continuity and fuzzifying R-map.

Keywords: Łukasiewicz logic,Fuzzifying topology,Fuzzifying regular open set,fuzzifying compact spaces,nearly compact spaces

### Article

Int. J. Fuzzy Log. Intell. Syst. 2010; 10(4): 296-302

Published online December 1, 2010

## On Fuzzifying Nearly Compact Spaces

A.M. Zahran,O.R. Sayed,M. Azab Abd-Allah,A.K. Mousa

### Abstract

This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies) introduced by Ying [16, (I)]. It investigates topological notions defined by means of regular open sets when these are planted into the framework of Ying's fuzzifying topological spaces (in Łukasiewwicz fuzzy logic). The concept of fuzzifying nearly compact spaces is introduced and some of its properties are obtained. We use the finite intersection property to give a characterization of fuzzifying nearly compact spaces. Furthermore, we study the image of fuzzifying nearly compact spaces under fuzzifying completely continuous functions, fuzzifying almost continuity and fuzzifying R-map.

Keywords: Łukasiewicz logic,Fuzzifying topology,Fuzzifying regular open set,fuzzifying compact spaces,nearly compact spaces