Some remarks on extraresolvable space
by
Salvador Garcia-Ferreira
National University of Mexico
Coauthors: R. A. Gonzalez-Silva (National University of Mexico)

A space X is said to be extraresolvable if X contains a family D of dense subsets such that |D | > \Delta(X) and the intersection of every two elements of D is nowhere dense, where \Delta(X) = min{ |U |: U  is  a  nonempty  open  subset  of  X }. We say that a space X is strongly extraresolvable if there is a family D of dense subsets of X such that |D \cap E | < nwd(X) whenever D and E are distinct elements of D, where nwd(X) = min{|A |: A subset or equal X, int_X(cl_XA) =/= \emptyset}. We give a countable extraresolvable space that is not strongly extraresolvable. We also prove that Q ×\omega₁ is strongly estraresolvable, and if X is strongly extraresolvable and nwd(X) = \Delta(X) = \omega, then X ×\omega is strongly extraresolvable (\omega₁ and \omega are equipped with the discrete topology).

Date received: February 14, 2000