One-point quasi-compactifications for fuzzy neighborhood spaces (Q1315867)

For a fuzzy neighbourhood space \((S, \Delta)\) a one-point ultra-quasi- compactification (ultra-compactification, quasi-compactification, compactification) \((\widehat S, \widehat \Delta)\) is defined. If a fuzzy neighbourhood space possesses a one-point compactification then it has infinitely many one-point compactifications. A general procedure for the construction of one-point quasi-compactifications of fuzzy neighbourhood spaces is described. A general one-point ultra-quasi-compactification is created. The Alexandroff theorem on quasi-compactifications is extended to fuzzy neighbourhood spaces.