Open AccessA Note on Strongly Lower Semi-Continuous Functions and the Induced Fuzzy Topological Space Generated by Them
Author(s) -
Apu Kumar Saha,
Debasish Bhattacharya
Publication year - 2013
Publication title -
journal of mathematical and fundamental sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.216
H-Index - 12
eISSN - 2337-5760
pISSN - 2338-5510
DOI - 10.5614/j.math.fund.sci.2013.45.1.6
Subject(s) - topological space , infimum and supremum , mathematics , topology (electrical circuits) , space (punctuation) , connected space , fuzzy logic , topological vector space , isolated point , pure mathematics , discrete mathematics , computer science , combinatorics , artificial intelligence , operating system
A new class of functions called strongly lower semi-continuous (SLSC) functions is defined and its properties are studied. It is shown that the arbitrary supremum and finite infimum of SLSC functions are again SLSC. Using these functions, an induced fuzzy topological space, called s-induced fuzzy topological space on a topological space (X, T), is introduced. Moreover, some incorrect results on fuzzy topological spaces obtained previously by some authors are identified and modified accordingly. Examples of the newly defined induced space are given and their various properties are investigated. Interrelationships between a fuzzy topological space (X, F) and the s-induced fuzzy topological space generated by the crisp members of F are examined. In this process, different lower semi-continuities and induced fuzzy spaces generated by them have been defined in a general set up and their few properties have been studied.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom