STRONG dq-REFINABILITY AND PROPERTY  OF INVERSE LIMITS

Keiko Chiba (Japan)

Received November 27, 2007

Abstract

Let  be an inverse system of spaces and X its inverse limit and let l denote the cardinal number of L. Then we show: (1) Suppose X is l-paracompact and each projection  is a pseudo-open map. If each  is strongly dq-refinable, then so is X. (2) Suppose X is hereditarily l-paracompact. If each  is hereditarily strongly dq-refinable, then so is X. (3) Suppose X is l-paracompact and subnormal and each projection  is a pseudo-open map. If each  has property  then so has X. (4) Suppose X is hereditarily l-paracompact and subnormal. If each  has hereditarily property  then so has X.

Keywords and phrases: inverse limit, strongly dq-refinable, property