Theorems on mappings satisfying a rational inequality
A phantom mapping h from a space Z to a space Y is a mapping whose restrictions to compact subsets are homotopic to constant mappings. If the mapping h is not homotopic to a constant mapping, one speaks of an essential phantom mapping. The definition of (essential) phantom pairs of mappings is analogous. In the study of phantom mappings (phantom pairs of mappings), of primary interest is the case when Z and Y are CW-complexes. In a previous paper it was shown that there are no essential phantom...
We use topological consequences of PFA, MA(S)[S] and PFA(S)[S] proved by other authors to show that normal first countable linearly H-closed spaces with various additional properties are compact in these models.