Abstract
In this paper, properties of connectedness on completely distributive topological lattices (Definition 2.1) and fuzzy topological spaces [1] are studied. Some equivalent propositions on the concepts of functions in completely distributive lattices, and connected elements in completely distributive lattices and fuzzy topological spaces are proved. Specially, connectedness is characterized both by the R-neighborhoods of molecules and C-separations. For any family {( L i , τ i ): i ϵ I} of fuzzy topological spaces, the product [1] ⊗ is connected iff every ( L i , τ i ) is connected. A continuous function maps connected elements onto connected ones. The connectedness on the fuzzy real line R ( L) is discussed in the last section as an important example. The intervals defined here (Definition 4.1) must be connected in the fuzzy real line R ( L), and so the intervals defined by Rodabaugh in [13] are too. Any connected element is connected in the fuzzy real line R ( L), if and only if R ( L) ⋍ R .
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
