IJPAM: Volume 118, No. 4 (2018)

Title

CERTAIN CONCEPTS IN FUZZY TOPOLOGY
VIA FUZZY PREOPEN SETS

Authors

Anjana Bhattacharyya
$^1$Department of Mathematics
Victoria Institution (College)
78B, A.P.C. Road, Kolkata, 700009, INDIA

Abstract

In 1991, S., Nanda introduced fuzzy preopen set. Using this concept, here we first introduce fuzzy regular preopen set, the collection of which is strictly larger than that of fuzzy preopen sets. Also some properties of fuzzy regular preopen sets are investigated here. Afterwards, a new type of fuzzy space, viz., fuzzy $p$-space is introduced in which finite intersection property of fuzzy regular preopen sets are true. In Section 2, we also introduced fuzzy regular $p$-space in which the collection of fuzzy preopen sets and fuzzy regular preopen sets are identical. In Section 3, we introduce fuzzy semi regular preopen set, the collection of which is strictly larger than that of fuzzy regular preopen sets. Also fuzzy extremally $p$-disconnected space is introduced in which every fuzzy regular preopen set is fuzzy preclopen.

History

Received: September 29, 2016
Revised: May 27, 2018
Published: May 31, 2018

AMS Classification, Key Words

AMS Subject Classification: 03E72
Key Words and Phrases: Fuzzy regular preopen set, fuzzy $p$-space, fuzzy semi regular preopen set, fuzzy regular $p$-space, fuzzy extremally $p$-disconnected space.

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1
Anjana Bhattacharyya, $p^{*}$-closure operator and $p^{*}$-regularity in fuzzy setting, Mathematica Moravica, 19 (1)(2015), 131-139.

2
C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182-190.

3
S. Nanda, Strongly compact fuzzy topological spaces, Fuzzy Sets and Systems, 42 (1991), 259-262.

4
Pao Ming Pu and Ying Ming Liu, Fuzzy topology I. Neighbourhood structure of a fuzzy point and Moore-Smith Convergence, J. Math Anal. Appl., 76 (1980), 571-599.

5
L.A. Zadeh, Fuzzy Sets, Inform. Control, 8 (1965), 338-353.

How to Cite?

DOI: 10.12732/ijpam.v118i4.20 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 118
Issue: 4
Pages: 1083 - 1090


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).