We prove a related fixed point theorem for n mappings which arenot necessarily continuous in n fuzzy metric spaces using an implicit relationone of them is a sequentially compact fuzzy metric space which generalizeresults of Aliouche, et al. [2], Rao et al. [14] and [15].

The set of point sets of R, n > 1, having the property that their minimal interpoint distance is greater than a given strictly positive constant is shown to be equippable by a metric for which it is a compact topological space. We also show that its subsets of Delone sets of given constants in R, n > 1, are compact. We prove that this result implies the classical selection theorem of Mahler.

Suppose that (X, g) is a conformally compact (n+1)-dimensional manifold that is hyperbolic near infinity in the sense that the sectional curvatures of g are identically equal to minus one outside of a compact set K ⊂ X. We prove that the counting function for the resolvent resonances has maximal order of growth (n + 1) generically for such manifolds. This is achieved by constructing explicit ex...

A compact domain in R n is a spectral set if there is some subset of R n such that fexp(2ih; xi) : 2 g when restricted to gives an orthogonal basis of L 2 ((). The set is called a spectrum for. We give a criterion for being a spectrum of a given set in terms of tiling Fourier space by translates of a suitable auxiliary set D. We apply this criterion to classify all spectra for the n-cube by sho...

We prove that for every M,N ∈ N, if τ is a Borel, finite, absolutely friendly measure supported on a compact subset K of R , then K ∩ BA(M,N) is a winning set in Schmidt’s game sense played on K, where BA(M,N) is the set of badly approximable M × N matrices. As an immediate consequence we have the following application. If K is the attractor of an irreducible finite family of contracting simila...

Conjunctive Boolean queries are a fundamental operation in web search engines. These queries can be reduced to the problem of intersecting ordered sets of integers, where each set represents the documents containing one of the query terms. But there is tension between the desire to store the lists effectively, in a compressed form, and the desire to carry out intersection operations efficiently...

Let K and L be compact convex sets in Rn. The following two statements are shown to be equivalent: (i) For every polytope Q ⊆ K having at most n+ 1 vertices, L contains a translate of Q. (ii) L contains a translate of K. Let 1 ≤ d ≤ n − 1. It is also shown that the following two statements are equivalent: (i) For every polytope Q ⊆ K having at most d+ 1 vertices, L contains a translate of Q. (i...

Exercise 1 (Maximal compact subgroups of G). A lattice in Qp is a finitelygenerated Zp-submodule of Qp that generates Qp as vector space. In particular, it’s free of rank n. Note that G acts transitively on the set of lattices in Qp . (i) Show that K = StabG(Zp ). (ii) Suppose that K ′ is a compact subgroup of G. Show that K ′ stabilises a lattice. (Hint: show that the K ′-orbit of Zp is finite...

Let M be the countably infinite metric fan. We show that Ck(M, 2) is sequential and contains a closed copy of Arens space S2. It follows that if X is metrizable but not locally compact, then Ck(X) contains a closed copy of S2, and hence does not have the property AP. We also show that, for any zero-dimensional Polish space X, Ck(X, 2) is sequential if and only if X is either locally compact or ...