We give two proofs that the 3–torus is not weakly d–congruent to #S × S, if d > 2. We study how cohomology ring structure relates to weak congruence. We give an example of three 3–manifolds which are weakly 5–congruent but are not 5–congruent. Let d be an integer greater than one. In [G], we considered two equivalence relations generated by restricted surgeries on oriented closed 3–manifolds. W...

in this paper, the notion of $psi -$weak contraction cite{rhoades} isextended to fuzzy metric spaces. the existence of common fixed points fortwo mappings is established where one mapping is $psi -$weak contractionwith respect to another mapping on a fuzzy metric space. our resultgeneralizes a result of gregori and sapena cite{gregori}.

We discuss new ways of characterizing, as maximal xed points of monotone operators, observational congruences on-terms and, more in general, equivalences on applicative structures. These characterizations naturally induce new forms of coinduction principles, for reasoning on program equivalences, which are not based on Abramsky's applicative bisimulation. We discuss in particular, what we call,...

Abstract We consider the implementation problem for incomplete information and private values. investigate double implementability of social choice functions in dominant strategy equilibria ex-post equilibria. define a new strategic axiom that implies “strategy-proofness” is implied by “secure strategy-proofness,” but converse these relationships does not hold. call it “weak secure-strategy-pro...

In this note first we define the notions of fuzzy positive implicativehyper BCK-ideals of types 1,2,3 and 4. Then we prove some theorems whichcharacterize the above notions according to the level subsets. Also we obtainthe relationships among these notions, fuzzy (strong, weak, reflexive) hyperBCK-ideals and fuzzy positive implicative hyper BCK-ideals of types 5,6,7and 8. Then, we define the no...

This paper takes choice theory to risk or uncertainty. Well-known decision models are axiomatized under the premise that agents can randomize. Under a reversal of order assumption, this convexifies choice sets, and even after imposing the weak axiom of revealed preference and nonemptiness of choice correspondences, the preferences directly revealed by choice may be incomplete or cyclical. Choic...

A fuzzy ideal on a set X is a non empty collection of subsets of X with heredity property which is also closed under arbitrary union and finite intersections. In this paper, we introduce a weak form of fuzzy ideals namely fuzzy pre-ideals and a way to obtain new fuzzy topologies is presented in this paper. Furthermore some interesting results for fuzzy ideals are generalized to fuzzy pre-ideal.