On zero dimensionality in fuzzy topological spaces
Different concepts of zero dimensionality in fuzzy topological spaces are studied. The \(c\)-zero (strongly \(c\)-zero) dimensionality, studied by \textit{N. Ajmal} and \textit{J. K. Kohli} [ibid. 61, No. 2, 231-237 (1994; Zbl 0847.54008)] in fuzzy topological spaces, is not a ``good extension'' of the zero small (large) inductive dimension in topological spaces. A fuzzy topological space \(X\) is strongly \(c\)-zero dimensional iff \(\dim_f X=0\). If each \(A_i\) is a closed, strongly \(c\)-zero dimensional fuzzy subspace of a fuzzy topological space \(X= \bigcup_{i=1}^n A_i\), then \(X\) is strongly \(c\)-zero dimensional.
scientific article; zbMATH DE number 1064294