Abstract:We discuss various results on the existence of `true' preimages under continuous open maps between $F$-spaces, $F$-lattices and some other spaces. The aim of the paper is to provide accessible proofs of this sort of results for functional-analysts.
Keywords: preimage; open map; complete metric space; $F$-space; $F$-lattice; compact set; uniformly open map; surpositive operator; lower semicontinuous set-valued map
DOI: DOI 10.14712/1213-7243.2020.007
AMS Subject Classification: 46A16 46A30 54E35 54E40 54E45 54E50 54D65 54C10