Abstract: The aim of this paper is to study the relations among soft topological spaces, soft L -topological spaces and stratified soft L -topological spaces. Firstly, we construct a Galois correspondence between the category SoTop of soft topological spaces and the category So L -Top of soft L -topological spaces, and obtain that SoTop is a coreflective subcategory of So L -Top . Secondly, we show that there is a Galois correspondence between the category SSo L -Top of stratified soft L -topological spaces and SoTop and obtain that SoTop is a reflective subcategory of SSo L -Top . Finally, we…study the stratification of soft L -topological spaces. We also construct a Galois correspondence between SSo L -Top and So L -Top , and obtain that SSo L -Top is a coreflective subcategory of So L -Top .
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Abstract: Based on fuzzy inclusion order between L -subsets, stratified L -ordered uniform convergence spaces and stratified L -ordered limit spaces are introduced. It is shown that the resulting categories are all Cartesian closed topological categories. Also, the relationship among stratified L -ordered limit spaces, stratified L -ordered Cauchy spaces and stratified L -ordered uniform convergence spaces are investigated.
Abstract: By using the residual implication on a frame L , a degree approach to special mappings in L -convex spaces and L -interval spaces is introduced. In the framework of L -convex spaces, degrees of L -CP mappings and L -CC mappings between L -convex spaces are defined. Also, in the situation of L -interval spaces, degrees of L -IP mappings and L -AIP mappings are proposed. Moreover, many conclusions with respect to theses mappings are discussed in a degree sense.