In this paper,we first defined an important concept of convergence on l * module,which is a double lattice ordered algebraic sturcture,then discussed the properties about the convergence,finally built up a topology na...In this paper,we first defined an important concept of convergence on l * module,which is a double lattice ordered algebraic sturcture,then discussed the properties about the convergence,finally built up a topology named l * topology.展开更多
A new method of constructing bornological vector topologies for vector spaces is discussed.In general,the convergent sequence and bounded set are concepts only in topological spaces.However,in this paper,it is first i...A new method of constructing bornological vector topologies for vector spaces is discussed.In general,the convergent sequence and bounded set are concepts only in topological spaces.However,in this paper,it is first introduced sequential convergence C and L * space which is a vector space giving some relation:x mCx between sequences and points in it,then the bounded set is defined in vector space.Let C be a sequential convergence,T(C) be a vector topology on X determined by C and B(C) be the collection of bounded sets determined by C.Then B(C)=B(T(C)).Furthermore,the bornological locally convex topological vector space is constructed by L * vector space.展开更多
In this paper we give a characteristic property of convergence of nets in induced I(L)-topological spaces and a simplified proof for the N-compactness being an I(L)-'good extension'.
文摘In this paper,we first defined an important concept of convergence on l * module,which is a double lattice ordered algebraic sturcture,then discussed the properties about the convergence,finally built up a topology named l * topology.
文摘A new method of constructing bornological vector topologies for vector spaces is discussed.In general,the convergent sequence and bounded set are concepts only in topological spaces.However,in this paper,it is first introduced sequential convergence C and L * space which is a vector space giving some relation:x mCx between sequences and points in it,then the bounded set is defined in vector space.Let C be a sequential convergence,T(C) be a vector topology on X determined by C and B(C) be the collection of bounded sets determined by C.Then B(C)=B(T(C)).Furthermore,the bornological locally convex topological vector space is constructed by L * vector space.
基金National Natural Science Foundation of China (10371079)
文摘In this paper we give a characteristic property of convergence of nets in induced I(L)-topological spaces and a simplified proof for the N-compactness being an I(L)-'good extension'.
