Abstract
In [3] we defined a notion of compactness in FCS, the category of fuzzy convergence spaces as defined by Lowen/Lowen/Wuyts [8]. In their paper the latter also introduced a fuzzy convergence structure c-lim for fuzzy function spaces thus proving that FCS is a topological quasitopos. In this paper we start the investigation of compactness criteria of the Arzelà-Ascoli type in these fuzzy function spaces. To this aim we first give a coarser fuzzy convergence structure p-lim of pointwise convergence, for which compactness is easily established (via the Tychonoff theorem) and then secondly introduce a notion of evenly continuous fuzzy subsets on which p-lim and c-lim coincide.
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.
