A note on uniformly locally connected open sets

Addition and reduction theorems for medial properties

“…For example, it is known that if a closed set separates «-space into two ulc" domains of which it is common boundary, then it is lc* [5] ; this is an immediate corollary of Theorem 3.10, since ulcfc domains have lcfc closures [5, p. 301, Theorem 5.8] and hence closures having property (P, Q)k. Even more generally, however, it follows from Theorem 3.10 that if any locally compact space is known to be lck + 1 and is separated into ulck open subsets by a common boundary B thereof (see [2]), then B is lck. Also, it follows from Theorem 3.10 that if a locally compact space X having property (P, Q)1 is the union of closed subsets Xu X2 having (P, Q)0, then Xl n X2 is locally connected.…”