Compactness and connectedness as absolute properties in fuzzy topological spaces

In general topology, a property P is called "absolute" iff for all subspaces Z subset of or equal to Y subset of or equal to X of a space X, Z fulfills P as a subspace of Y iff Z fulfills P as a subspace of X, e.g. compactness and connectedness are absolute properties. In this paper, a setting for fuzzy topology is given in which the two most successful fuzzy compactnesses, i.e. Chadwick's f-compactness (1991) and Wang's N-compactness (1983) are shown to be absolute. A new definition of fuzzy connectedness is given and proved to be equivalent to Pu and Liu's definition (1980), thus showing that the latter is also absolute. (C) 1998 Elsevier Science B.V.