semi-regular locales are extensions of the classical semiregularspaces. we investigate the conditions such that semi-regularizationis a functor. we also investigate the conditions such that semi-regularizationis a reflection or coreflection.

in this study, we investigate the further properties of quasi irresolute topological groupsdened in [20]. we show that if a group homomorphism f between quasi irresolute topologicalgroups is irresolute at eg, then f is irresolute on g. later we prove that in a semi-connectedquasi irresolute topological group (g; ; ), if v is any symmetric semi-open neighborhood ofeg, then g is generated by v...

the polynomial interpolation in one dimensional space r is an important method to approximate the functions. the lagrange and newton methods are two well known types of interpolations. in this work, we describe the semi inherited interpolation for approximating the values of a function. in this case, the interpolation matrix has the semi inherited lu factorization.

Each closed oriented 3-manifoldM is naturally associated with a set of integersD(M), the degrees of all self-maps on M . D(M) is determined for each torus bundle and torus semi-bundle M . The structure of torus semi-bundle is studied in detail. The paper is a part of a project to determine D(M) for all 3-manifolds in Thurston’s picture.

Ever since the introduction of fuzzy sets by L. A. Zadeh [14], the fuzzy concept has invaded almost all branches of Mathematics. The concept of fuzzy topological space was introduced and developed by C.L. Chang [3] and since then many fuzzy topologists [1,6-13] have extended various notions in classical topology to fuzzy topological spaces. The concept of somewhat continuous functions was intro...

A subset A of a space X is called regular open if A = IntA, and regular closed if X\A is regular open, or equivalently, if A= IntA. A is called semiopen [16] (resp., preopen [17], semi-preopen [3], b-open [4]) ifA⊂ IntA (resp.,A⊂ IntA,A⊂ IntA ,A⊂ IntA∪ IntA). The concept of a preopen set was introduced in [6] where the term locally dense was used and the concept of a semi-preopen set was introd...