We study mechanism which operate on ordinal preference information (i.e., rank ordered lists of alternatives) on the full domain of weak preferences that admits indifferences. We present a novel decomposition of strategyproofness into three axioms: separation monotonic, separation upper invariant, and separation lower invariant. Each axiom is a natural restriction on how mechanisms can react wh...

In this paper, given a nonadditive measure ? , topology, which is compatible with convergence in -measure, defined on the real linear space of all (equivalence classes of) measurable functions by using distance introduced Dunford and Schwartz. Some fundamental properties such as open sphere condition, Hausdorff separation axiom, separability, approximation continuous functions, linearlization, ...

We discuss a notion of universe in toposes which from a logical point of view gives rise to an extension of Higher Order Intuitionistic Arithmetic (HAH) that allows one to construct families of types in such a universe by structural recursion and to quantify over such families. Further, we show that (hierarchies of) such universes do exist in all sheaf and realizability toposes but neither in t...

In this paper, we define and investigate the notions of πgI-closed sets and πgI-open sets in ideal topological spaces. Then, we define ∨π-sets and ∧π-sets and discuss the relation between them. Also, we give characterizations of πgI-closed sets and πgs-closed sets. A separation axiom stronger than πTI -space is defined and various characterizations are given.

The bitopological unstability of RR-pairwise paracompactness in presence of pairwise Hausdorff separation axiom is caused by a bitopological property which is much weaker and more local than RR-pairwise paracompactness. We slightly generalize some Michael’s constructions and characterizeRR-pairwise paracompactness in terms of bitopological θ-regularity, and some other weaker modifications of pa...

In this paper, an O-convergence theory of fuzzy nets is built in L-topological spaces by means of neighborhoods of fuzzy points. It has many nice properties. It can be used to characterize the closed set, open set, T2 separation axiom and fuzzy compactness. c © 2003 Elsevier B.V. All rights reserved.

In 1948 Miroslav Katětov showed that if the cube X3 of a compact space X satisfies the separation axiom T5 then X must be metrizable. He asked whether X3 can be replaced by X2 in this metrization result. In this note we prove the consistency of this implication.

In this paper we will prove the Urysohn Meterization Theorem, which gives sufficient conditions for a topological space to be metrizable. In the process of proving this theorem, we will the discuss separation and countability axiom of topological spaces and prove the Urysohn Lemma.

This article continues the study of computable elementary topology started in [7]. We introduce a number of computable versions of the topological T0 to T3 separation axioms and solve their logical relation completely. In particular, it turns out that computable T1 is equivalent to computable T2. The strongest axiom SCT3 is used in [2] to construct a computable metric.

Several axioms concerning probabilistic beliefs are examined here, and the relations between them are established, using belief spaces that generalize Harsanyi type spaces. Two axioms concerning highorder probabilistic beliefs are investigated in particular. The first is the triviality axiom, which says that one is certain (that is, has a belief of degree one) of one’s own beliefs. The second i...