Local Topological Properties and One Point Extensions

Abstract

In 1957, Mrowka [ 12 ] showed that a locally paracompact space admits a one point paracompactification (see also [ 2 , Chapter 9, § 4, Exercise 27]). Similarly, in [ 9 ] Isiwata obtained a one point realcompactincation for locally realcompact spaces. Recently a number of authors (see [ 11, 16; 17; 18; 21 ]) have constructed one point P -extensions of local P -spaces for a variety of topological properties P . It is the purpose of this paper to draw together the various techniques used by the above mentioned authors and to study the set (lattice) of all one point P -extensions of a particular space.