In particular,if (L~X,δ)is a ,λ-weakly induced space,then (L~X,δ)is a Hausdorff space or a strongly Hausdorff space. iff the λ-cut topological space(X,l_λ(δ))is a Hausdorff space,hence,in the class of λ-weakly induced spaces,Hausdorff separation is equivalent to strongly Hausdorff separation;

In this article,we prove the subdirect product representation theorem of complete rings of sets and the following result:An induced space (LX,T ) is completely regular its underlying space (X,［T ］) is comletely regular.

if ( L X,δ ) is a fully_sheaved and λ _weakly induced space, then (L X,δ) is a ST 2_space, if and only if it is a strongly Hausdorff space, the λ _cut topological space ( X,ι λ(δ) ) is a Hausdorff space,and the base space ( X,) is a Hausdorff space.

In the light of the F strong paracompactness concept,it is proved that the F strong paracompact space with strong Hausdorff is a weakly induced space. As a corollary,it is showed that the F strong paracompact space with strong Hausdorff separation is Strongly normal.

用 F 强仿紧性的概念,证明了强 Hausdorff 的 F 强仿紧空间是弱诱导的,并由此推出强 Hausdorff 的 F 强仿紧空间是强正规的.

For the linear log contrast model with mixture's design space, a transforma tion is made first and the an induced space is founded in this paper. An optimal value in this space is given and the design responding to the value is proved to be a D──optimal design,

The multiplication of containwise regular spaces is discussed. The results that the containwise regularity of an induced space is equivalent to the regularity of its induced space under the condition of closure preservuing and that containwise regularity is a good extension in the sense of Lowen are obtained.

When the driving frequency is high enough, a large number of ions are trapped and the induced space charge field makes a great many of electrons stay in the discharge volume.

Toward a factually induced space-time quantum logic

Experimental Assessment of the Nonuniform Radiation-Induced Space-Charge Distribution in the Surface Region of Silicon

As usual in laser stereophotolithography or laser microstereophotolithography, the part is manufactured layer by layer by a light-induced space-resolved polymerization.

The laser stereophotolithography is a process which allows the manufacture of 3D parts by a light-induced space-resolved polymerization.

The laser stereophotolithography is a process which allows the manufacture of 3D parts by a light-induced space-resolved polymerization.

It is the purpose of this paper to survey the known results about the fuzzy unit interval I(L). I(L) is a rather unique fuzzy topological space and possesses many important properties, for example, it can be used to characterize fuzzy normality and uniformizability. Theseresults are arranged in four sections as follows: §1 , Introductionof the fuzzy unit interval; §2, Topological properties of the fuzzyunit interval and its applications on Stone-Cech compactification;§3, Lattice-theoretical properties...

It is the purpose of this paper to survey the known results about the fuzzy unit interval I(L). I(L) is a rather unique fuzzy topological space and possesses many important properties, for example, it can be used to characterize fuzzy normality and uniformizability. Theseresults are arranged in four sections as follows: §1 , Introductionof the fuzzy unit interval; §2, Topological properties of the fuzzyunit interval and its applications on Stone-Cech compactification;§3, Lattice-theoretical properties and algebraic operation;§4, I(L)value semi-continuous functions and induced spaces.

In the present paper,the systematic theory of L-valued lower semicontinuous functions has been discussed.For a fixed set X,the writer established the map ω_L from the set ■(X) of crisp toplogies on X to the set △(X,L) of L-fuzzy topologies on X, and the map l_L from △(X,L)to■(X).The properties of ω_L and l_L are discussed. especially the structure of the base for ω_L(■)is clarified.As the appliction of the theory,the author obtained a series of results about the relation between induced spaces and their...

In the present paper,the systematic theory of L-valued lower semicontinuous functions has been discussed.For a fixed set X,the writer established the map ω_L from the set ■(X) of crisp toplogies on X to the set △(X,L) of L-fuzzy topologies on X, and the map l_L from △(X,L)to■(X).The properties of ω_L and l_L are discussed. especially the structure of the base for ω_L(■)is clarified.As the appliction of the theory,the author obtained a series of results about the relation between induced spaces and their generated spaces,for example,the subspaces,product spaces and quotient spaces of induced spaces are all induced spaces.

本文系统地讨论了格值下半连续函数理论.对于给定集合 X,建立 X 上分明拓扑的全体 T(X)到 X 上的 L-fuzzy 拓扑的全体Δ(X,L)上的映射ω_L 和由Δ(X,L)到 T(X)的映射ι_L.讨论了ω_L 和ι_L 的性质,特别是给出了ω_L(■)的基的结构.作为应用,建立了可拓扑生成空间与其生成空间之间关系的一系列结果,例如,可拓扑生成空间的子空间、积空间、商空间等也是可拓扑生成的.

In this paper, starting with the stratum structure of L-fuzzy topological spaces, we define the spaces in which closure operators preserve strata. By useing of this conception, we give out some equivalent conditions for the commutativity of closure operators with the product operator in fully stratified L-fuzzy topological spaces, and prove that: if each factor space of a product space is induced space, then the closure operators are commutative with the product operator, therefor the problem put forward...

In this paper, starting with the stratum structure of L-fuzzy topological spaces, we define the spaces in which closure operators preserve strata. By useing of this conception, we give out some equivalent conditions for the commutativity of closure operators with the product operator in fully stratified L-fuzzy topological spaces, and prove that: if each factor space of a product space is induced space, then the closure operators are commutative with the product operator, therefor the problem put forward in [2] has been well solved.