Our first purpose in this paper is to provide necessary conditions for a weak＊-closed translation invariant subspace in the semigroup algebra of a locally compact topological foundation semigroup to be completely com...Our first purpose in this paper is to provide necessary conditions for a weak＊-closed translation invariant subspace in the semigroup algebra of a locally compact topological foundation semigroup to be completely complemented. We give conditions when a weak＊-closed left translation invariant subspace in Ma,（S）＊ of a compact cancellative foundation semigroup S is the range of a weak＊-weak＊ continuous projection on M~,（S）＊ commuting with translations. Let G be a locally compact group and A be a Banach G-module. Our second purpose in this paper is to study some projections on A＊ and /3（A＊） which commutes with translations and convolution.展开更多
This article aims to present new terms of single-valued neutrosophic notions in theˇSostak sense,known as singlevalued neutrosophic regularity spaces.Concepts such as r-single-valued neutrosophic semi￡-open,r-single...This article aims to present new terms of single-valued neutrosophic notions in theˇSostak sense,known as singlevalued neutrosophic regularity spaces.Concepts such as r-single-valued neutrosophic semi￡-open,r-single-valued neutrosophic pre-￡-open,r-single valued neutrosophic regular-￡-open and r-single valued neutrosophicα￡-open are defined and their properties are studied as well as the relationship between them.Moreover,we introduce the concept of r-single valued neutrosophicθ￡-cluster point and r-single-valued neutrosophicγ￡-cluster point,r-θ￡-closed,andθ￡-closure operators and study some of their properties.Also,we present and investigate the notions of r-single-valued neutrosophicθ￡-connectedness and r-single valued neutrosophicδ￡-connectedness and investigate relationship with single-valued neutrosophic almost￡-regular.We compare all these forms of connectedness and investigate their properties in single-valued neutrosophic semiregular and single-valued neutrosophic almost regular in neutrosophic ideal topological spaces inˇSostak sense.The usefulness of these concepts are incorporated to multiple attribute groups of comparison within the connectedness and separateness ofθ￡andδ￡.展开更多
In this paper we develop a theory of localization for bounded commutative BCK-algebras. We try to extend some results from the case of commutative Hilbert algebras (see [1]) to the case of commutative BCK-alge- bras.
文摘Our first purpose in this paper is to provide necessary conditions for a weak＊-closed translation invariant subspace in the semigroup algebra of a locally compact topological foundation semigroup to be completely complemented. We give conditions when a weak＊-closed left translation invariant subspace in Ma,（S）＊ of a compact cancellative foundation semigroup S is the range of a weak＊-weak＊ continuous projection on M~,（S）＊ commuting with translations. Let G be a locally compact group and A be a Banach G-module. Our second purpose in this paper is to study some projections on A＊ and /3（A＊） which commutes with translations and convolution.
文摘This article aims to present new terms of single-valued neutrosophic notions in theˇSostak sense,known as singlevalued neutrosophic regularity spaces.Concepts such as r-single-valued neutrosophic semi￡-open,r-single-valued neutrosophic pre-￡-open,r-single valued neutrosophic regular-￡-open and r-single valued neutrosophicα￡-open are defined and their properties are studied as well as the relationship between them.Moreover,we introduce the concept of r-single valued neutrosophicθ￡-cluster point and r-single-valued neutrosophicγ￡-cluster point,r-θ￡-closed,andθ￡-closure operators and study some of their properties.Also,we present and investigate the notions of r-single-valued neutrosophicθ￡-connectedness and r-single valued neutrosophicδ￡-connectedness and investigate relationship with single-valued neutrosophic almost￡-regular.We compare all these forms of connectedness and investigate their properties in single-valued neutrosophic semiregular and single-valued neutrosophic almost regular in neutrosophic ideal topological spaces inˇSostak sense.The usefulness of these concepts are incorporated to multiple attribute groups of comparison within the connectedness and separateness ofθ￡andδ￡.
文摘In this paper we develop a theory of localization for bounded commutative BCK-algebras. We try to extend some results from the case of commutative Hilbert algebras (see [1]) to the case of commutative BCK-alge- bras.
