Mappings on weakly Lindelöf and weakly regular-Lindel¨of spaces
Keywords:Lindelöf, weakly Lindelöf and weakly regular-Lindel¨of space, Almost continuous and almost precontinuous functions
AbstractIn this paper we study the effect of mappings and some decompositions of continuity on weakly Lindelöf spaces and weakly regular-Lindelöf spaces. We show that some mappings preserve these topological properties. We also show that the image of a weakly Lindelöf space (resp. weakly regular-Lindelöf space) under an almost continuous mapping is weakly Lindelöf (resp. weakly regular-Lindelöf). Moreover, the image of a weakly regular-Lindelöf space under a precontinuous and contracontinuousmapping is Lindelöf.
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