Fuzzy Counterparts of Fischer Diagonal Condition in ?-Convergence Spaces

Qiu Jin, Lingqiang Li and Jing Jiang
Additional contact information
Qiu Jin: School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China
Lingqiang Li: School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China
Jing Jiang: School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China

Mathematics, 2019, vol. 7, issue 8, 1-18

Abstract: Fischer diagonal condition plays an important role in convergence space since it precisely ensures a convergence space to be a topological space. Generally, Fischer diagonal condition can be represented equivalently both by Kowalsky compression operator and Gähler compression operator. ?-convergence spaces are fundamental fuzzy extensions of convergence spaces. Quite recently, by extending Gähler compression operator to fuzzy case, Fang and Yue proposed a fuzzy counterpart of Fischer diagonal condition, and proved that ?-convergence space with their Fischer diagonal condition just characterizes strong L -topology—a type of fuzzy topology. In this paper, by extending the Kowalsky compression operator, we present a fuzzy counterpart of Fischer diagonal condition, and verify that a ?-convergence space with our Fischer diagonal condition precisely characterizes topological generated L -topology—a type of fuzzy topology. Hence, although the crisp Fischer diagonal conditions based on the Kowalsky compression operator and the on Gähler compression operator are equivalent, their fuzzy counterparts are not equivalent since they describe different types of fuzzy topologies. This indicates that the fuzzy topology (convergence) is more complex and varied than the crisp topology (convergence).

Keywords: fuzzy topology; fuzzy convergence; ?-convergence; diagonal condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/8/685/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/8/685/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:8:p:685-:d:253482

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().