Local Compactness in Fuzzy Convergence Spaces

Two notions of local precompactness in the realm of fuzzy convergence spaces are investigated. It is shown that the property of local precompactness possesses a ‘‘good extension.’’ Moreover, for each given fuzzy convergence space, there exists a coarsest locally precompact space which is finer than the original space. Continuity between fuzzy spaces is preserved between the associated locally precompact spaces. Invariance of regularity with respect to taking locally precompact modifications is discussed.