A NOTE ON PARACOMPACT p-SPACES AND THE MONOTONE D-PROPERTY

Abstract

For any generalized ordered space X with the underlying linearly ordered topological space X u , let X * be the minimal closed linearly ordered extension of X andX be the minimal dense linearly ordered extension of X . The following results are obtained.(1)The projection mapping π :The projection mapping φ :X → X u , φ( x, i ) = x, is closed. 2010 Mathematics subject classification: primary 54C10; secondary 54C25, 54D20, 54D30, 54F05.