On $m$-paracompact spaces and $\omega$-mappings

T. E. Gantner
1973 Canadian mathematical bulletin  
1. Introduction. The purpose of this note is to present a characterization of m-paracompact normal spaces in terms of co-mappings into m-separable metric spaces; this result is almost contained in Morita's original paper [2] and is implicitly contained in Shapiro's thesis paper [5] . This result is a natural generalization of the well-known Katetov-Ponomarev characterization of paracompact spaces (see [4] ), and a special case of it (when m= K 0 ) was recently discovered by Pareek [3] . If m is
more » ... an infinite cardinal number, then m-separable metric spaces are defined in [5] , and m-paracompact normal spaces are defined in [2] . For the concept of normal covers, see [7] , and for the term co-mapping, see [3] or [4]. 2. The theorem. Specifically, we augment Morita's Theorem 1.2 of [2] by proving the following.
doi:10.4153/cmb-1973-066-x fatcat:oyqi6wja55b3bj3nbysg2vymeq