Nonstandard Analysis Methods for Separations in [0,1]-topological Spaces

In nonstandard enlargement, the separations are characterized by non- standard analysis methods in [0, 1J-topological spaces. Firstly, the monads of fuzzy point in [0, 1]-topological spaces are described with remote-neighborhoods in non- standard enlarged model. Then the nonstandard characterizations of separations in [0, 1]-topological space are given by the monads. At last, relations of these separations are investigated.

LARGE DEVIATIONS FOR STATIONARY Φ-MIXING SEQUENCES IN τ-TOPOLOGY

The results of Bryc on large deviations for empirical measures of stationary Φ-mixing sequences are extended. Bryc states his results in the usual weak topology on the space ofprobability measures. In this paper, under somewhat weaker assumptions than those of Bryc,the author extends Bryc's results by taking the finer topology which is generated by the integralsover bounded measurable functions.

ε-isometric Approximation Problem

In this paper, some problems for isometric approximation are discussed. It is shown that an almost isometry from the unit ball of C(X) into the unit ball of C(Y) is near to an isometry. We also give a counterexample to this problem on the unit ball of l1.

＂From a Utopia to a Dystopia＂ On Mark Twain＇s Compliance with and Deviation from Heterotopology in A Connecticut Yankee in King Arthur＇s Court

In this paper, the author intends to parallelize Mark Twain＇s A Connecticut Yankee in King Arthur＇s Court with Foucault＇s theorizations about heterotopia, or heterotopology. For Foucault, heterotopia is a paradox because it is paces that are both real and placeless. Twain＇s novel is a time travel story, which juxtaposes the temporalities of the 6th and 19th centuries. In the story, Hank, the hero, is allowed access to Camelot, King Arthur＇s court. Above all, he has introduced to it quite a few elements of modem technology and civilization. So far Twain seems to have complied with Foucault＇s heterotopology. That is, there is a textual heterotopia created in his novel. However, the last principle of Foucault＇s heterotopology states that a heterotopia can be comparable to a utopia because of its contrastive function. A typical time travel story has the same contrastive function as well. That is, in either case there should be a utopia, a dystopia, or a mixture of them. However, Twain＇s novel fails to contrast the 6th century with the 19th century simply because the heterotopia Hank has created leaps from a utopia to a dystopia. It is at this point where Twain has deviated from heterotopology. The shifting nature of this heterotopia not only disables its contrastive mechanism but also jeopardizes its thematic clarity. Most of all, it indicates that Twain has a considerably ambivalent attitude towards the industrial civilization, and that as a consequence, he is indecisive about the direction of this novel.

On the Random Conjugate Spaces of a Random Locally Convex Module

Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two which are universally suitable for the current development of the theory of random conjugate spaces. In this process, we also obtain a somewhat surprising and crucial result： if the base （Ω,F, P） of a random normed module is nonatomic then the random normed module is a totally disconnected topological space when it is endowed with the locally L0-convex topology.

Limit theorems of continuous-time random walks with tails

We study the functional limits of continuous-time random walks （CTRWs） with tails under certain conditions. We find that the scaled CTRWs with tails converge weakly to an a-stable Levy process in D（[0, 1]） with M1-topology but the corresponding scaled CTRWs converge weakly to the same limit in D（[0, 1]） with J1-topology.