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Fuzzifying topology induced by Morsi fuzzy pseudo-norms.
- Source :
-
International Journal of General Systems . Aug2022, Vol. 51 Issue 6, p648-662. 15p. - Publication Year :
- 2022
-
Abstract
- The purpose of this paper is to endow the fuzzy pseudo-norm in the sense of Morsi with many-valued topological structures. It is shown that there exists a one-to-one correspondence between any fuzzy pseudo-norm given by Morsi and a family of left continuous and non-ascending pseudo-norms. Then a fuzzifying topology induced by Morsi fuzzy pseudo-norms is introduced, it is proved that this fuzzifying topology is compatible with the vector structure. Based on this many-valued topological structure, the degree to fuzzy normed space which is Hausdorff, the degree to a sequence which is convergent, and the degree to a set which is bounded are studied. The layered characterizations of them are presented. Finally, the conclusion which a linear operator is fuzzy continuous if and only if it is fuzzy bounded is proved. [ABSTRACT FROM AUTHOR]
- Subjects :
- *TOPOLOGY
*VECTOR topology
*LINEAR operators
Subjects
Details
- Language :
- English
- ISSN :
- 03081079
- Volume :
- 51
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- International Journal of General Systems
- Publication Type :
- Academic Journal
- Accession number :
- 158042046
- Full Text :
- https://doi.org/10.1080/03081079.2022.2052061