Fuzzifying topological linear spaces

In this paper, we establish a fundamental framework of fuzzifying topological linear spaces (abbreviated to ftls). After providing some fuzzy logical notations and some basic properties of fuzzifying topological spaces, we define a number of equivalent ftls, and discuss some of their basic propertie...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Fuzzy sets and systems Jg. 147; H. 2; S. 249 - 272
1. Verfasser: Qiu, Daowen
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 16.10.2004
Schlagworte:
Boundedness
Compactness
Fuzzy logic
Neighborhood
T2 separation axiom
Topological linear spaces
Topology
Fuzzy logic
Compactness
Boundedness
Topological linear spaces
Topology
T 2 separation axiom
Neighborhood
ISSN:0165-0114, 1872-6801
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:In this paper, we establish a fundamental framework of fuzzifying topological linear spaces (abbreviated to ftls). After providing some fuzzy logical notations and some basic properties of fuzzifying topological spaces, we define a number of equivalent ftls, and discuss some of their basic properties. Then we deal with the bases for fuzzifying neighborhood systems, and particularly verify a characterization of ftls by using the bases of fuzzifying neighborhood systems of original point 0. Also, we demonstrate two characterizations of T 2 separation axiom. After that, fuzzy boundedness and fuzzy complete boundedness are defined and some related properties are demonstrated; in particular, we prove an equivalent characterization of fuzzy boundedness. Furthermore, we study fuzzy compactness in ftls, and demonstrate that a subset A is compact if and only if it is completely bounded and any Cauchy net S in A converges at some point in A.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2003.10.024