ON REGULAR SEPARABLE COUNTABLY COMPACT R-RIGID SPACES

A topological space X is said to be Y-rigid if any continuous map f: X -> Y is constant. In this paper we construct a number of examples of regular countably compact Double-struck capital R-rigid spaces with additional properties like separability and first countability. This way we answer several questions of Tzannes, Banakh, Ravsky, as well as get a consistent example of Double-struck capital R-rigid Nyikos space. Also, we show that it is consistent with ZFC that for every cardinal kappa < c there exists a regular separable countably compact space X which is Y-rigid with respect to any T-1 space Y of pseudocharacter <= kappa.