Volume 28 • Number 2 • 2005     • Semicompactness in Fuzzy Topological Spaces R.P. Chakraborty, A. Bhattacharyya and M.N. Mukherjee Abstract. The paper deals with the concept of semicompactness in the generalized setting of a fuzzy topological space. We achieve a number of characterizations of a fuzzy semicompact space. The notion of semicompactness is further extended to arbitrary fuzzy sets. Such fuzzy sets are formulated in different ways and a few pertinent properties are discussed. Finally we compare semicompact fuzzy sets with some of the existing types of compact-like fuzzy sets. We ultimately show that so far as the mutual relationships among different existing allied classes of fuzzy sets are concerned, the class of semicompact fuzzy sets occupies a natural position in the hierarchy. 2000 Mathematics Subject Classification: 54A40; Secondary 54D99. Full text: PDF