Partition of topological spaces into zero-dimensional subsets
L. Grinblat, Togo Nishiura · Rocky Mountain Journal of Mathematics · 1980
The first results on the partition of topological spaces were achieved by Tumarkin [6].He proved that for any Euclidean space E n there exists a sequence {Y { } such that E» = Uëi Y-open?Clearly, the assertion is true if the space is hereditarily normal.The answer would be yes if the union of two Z)-open sets is a normal subspace.(See the proof of theorem 5 below.)DEFINITION 4. A basis 38 for a space X is said to be complete if (i) each member of J 1 is a cozero set of X and