Base-paracompactness and base-normality of ordered spaces
by
Gary Gruenhage
Auburn University

J.E. (Ted) Porter calls a space X base-paracompact iff there is a base B for X of cardinality equal to the weight of X such that every open cover U of X has a locally finite refinement by members of B. K. Yamazaki calls a normal space X base-normal iff there is a base B which satisfies the above statement restricted to two-element open covers U.

Porter showed that paracompact ordered spaces of weight not greater than aleph_1 are base-paracompact, and asked if all paracompact ordered spaces are base-paracompact. Yamazaki asked if all ordered spaces are base-normal. We show that the answer to Porter’s question is “yes”, but the answer to Yamazaki’s question is “no”.

Date received: March 1, 2005