Connectedness and dimension of GF-spaces (Q1192489)

The author continues his study of GF-spaces, which generalize fuzzy topological spaces by requiring that fuzzy sets fall between upper and lower bounds, perhaps not \(\chi_ \emptyset\) and \(\chi_ X\). He generalizes connectedness in the manner of \textit{U. V. Fatteh} and \textit{D. S. Bassan} [J. Math. Anal. Appl. 111, 449-464 (1985; Zbl 0588.54008)], defines dimension for GF-spaces, and proves some analogs of familiar theorems, e.g., a regular, zero-dimensional GF-space must be totally disconnected.