强满层L-收敛空间的一个注记

众所周知,强满层L-收敛空间自然是满层L-收敛空间,但反之不成立。给出了满层L-收敛空间成为强满层L-收敛空间的一个充要条件。给出了一种生成满层L-收敛空间的方法,并由此构造了一个从满层L-收敛空间到强满层L-收敛空间的具体的反射。

L-收敛空间(英文)

文中对任一具有逆序对合对应的完全分配格L引入了L 收敛空间的概念 ,主要证明了 :( 1)L 预拓扑空间范畴是F 对角L 收敛空间范畴的延拓式拓扑包 (extensionaltopologicalhull) .( 2 )L 伪拓扑空间范涛是F 对角L 收敛空间范畴的拓扑论域包 (topologicalunivereshull) .

L-SLLSC同构L-SSC

对层次满层L-收敛空间引入了强左连续条件,证明了强左连续的层次满层L-收敛空间范畴:可以反射嵌入到层次满层L-收敛空间范畴;恰好可以刻画强满层L-收敛空间范畴。

L-PC(CA)余反射嵌入L-SSC

构造了从概率L-收敛空间范畴到强满层的L-收敛空间范畴的一个嵌入函子,并证明了前者可以余反射嵌入后者.类似地,证明了当L=[0,1]时,收敛方式空间也可以余反射嵌入强满层的L-收敛空间.

L-模糊化收敛空间范畴的monoidal闭性

本文格值环境是完备剩余格L,当L是完备剩余格时,L-模糊化收敛空间范畴关于其上的张量积运算是monoidal闭的,从而具有所期望的函数空间。特别地,如果L是完备的Heyting代数,L-模糊化收敛空间范畴就是笛卡儿闭的。

L-滤子收敛结构的对角化条件

借助L-滤子给出了L-滤子收敛结构的对角化条件,并给出它的两种等价刻画。最后证明了L-滤子拓扑收敛空间和L-拓扑空间是范畴同构的。

METHOD OF CONSTRUCTING BORNOLOGICAL SPACES FROM L~*-VECTOR SPACES

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.

Convergence of Nets in Induced I(L)-Topological Spaces with an Application

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'.