Admissibility, homeomorphism extension and the AR-property in topological linear spaces
One of the main problems of the topology of vector spaces is to prove that every linear space has the absolute extension property (AE- property). Some relative properties are considered in the paper. One of them is the so-called homeomorphism extension property (HEP). It is proved that HEP for finite-dimensional compacta holds in every infinite- dimensional complete linear space and, even more, in every non-\(\sigma\)- compact linear space. Also it is proved that if there is a counterexample to the AE-conjecture for linear spaces then there is a counterexample to HEP. The other is so-called an admissibility which is very closely to the extension property for compact spaces. It is proved that HEP implies admissibility. The question ``Is every linear space admissible?'' is discussed.
scientific article; zbMATH DE number 149087
scientific article