Relative paracompactness and relative collectionwise normality
by
Jamal Tartir
Youngstown State University
Coauthors: Elise Grabner, Gary Grabner, Kazumi Miyazaki

A space Y is (1-) paracompact in X if every open cover of X has an (open refinement) open partial refinement which covers (X) Y and is locally finite with respect to Y. A space Y is collectionwise normal in a larger space X if for every discrete collection of closed sets {F_\alpha}_{\alpha in \Lambda} there is a collection of open sets {U_\alpha}_{\alpha in \Lambda} such that {U_\alpha}_{\alpha in \Lambda} is discrete with respect to Y and F_\alpha \cap Y subset or equal U_\alpha subset or equal X\ \cup _{\beta in \Lambda\{\alpha}}F_\beta for all \alpha in \Lambda.

Recent results and questions concerning various relationships between relative paracompactness and relative collectionwise normality will be discussed.

Date received: June 5, 2003