in the present paper we introduce and study the notion of pairwise weakly lindelof bitopological spaces and obtain some results. further, we also study the pairwise weakly lindelof subspaces and subsets, and investigate some of their properties. it was proved that a pairwise weakly lindelof property is not a hereditary property.

the pectic enzymes produced in vitro by 8 isolates (5 highly virulent and 3 weakly virulent) of fusarium oxysporum , were detected by spectrophotometry, and characterized by polyacrylamide gel electrophoresis with substrate-containing gels (zymogram). analysis of the polygalacturonase (pg) isozyme banding patterns (zymogram) identified two distinct phenotypes among the isolates from chickpea (c...

The pectic enzymes produced in vitro by 8 isolates (5 Highly virulent and 3 Weakly virulent) of Fusarium oxysporum , were detected by spectrophotometry, and characterized by polyacrylamide gel electrophoresis with substrate-containing gels (zymogram). Analysis of the polygalacturonase (PG) isozyme banding patterns (zymogram) identified two distinct phenotypes among the isolates from chickpea (C...

the theory of c-frames and c-bessel mappings are the generalizationsof the theory of frames and bessel sequences. in this paper, weobtain several equivalent conditions for dual of c-bessel mappings.we show that for a c-bessel mapping $f$, a retrievalformula with respect to a c-bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-besselmapping which  wea...

the aim of this paper is to introduce the concepts of fuzzy upper and fuzzy lower almost continuous, weakly continuous and almost weakly continuous multifunctions. several characterizations and properties of these multifunctions along with their mutual relationships are established in $l$-fuzzy topological spaces