We consider the following problem: given a set X and a function T : X → X, does there exist a compact Hausdorff topology on X which makes T continuous? We characterize such functions in terms of their orbit structure. Given the generality of the problem, the characterization turns out to be surprisingly simple and elegant. Amongst other results, we also characterize homeomorphisms on compact me...

A least absolute approach to multiple fuzzy regression using Tw-norm based arithmetic operations is discussed by using the generalized Hausdorff metric and it is investigated for the crisp inputfuzzy output data. A comparative study based on two data sets are presented using the proposed method using shape preserving operations with other existing method.

Our purpose is to deal with quadratic operators acting between vector lattices of continuous mappings on a compact Hausdorff space. In our first main result we characterize quadratic-multiplicative operators, whereas in the second one we provide necessary and sufficient conditions for a quadratic operator to be proportional to the square of a continuous linear operator.

We consider shape, size and regularity of the hulls Kt of the chordal Schramm-Loewner evolution driven by a symmetric α-stable process. We obtain derivative estimates, show that the domains H \Kt are Hölder domains, prove that Kt has Hausdorff dimension 1, and show that the trace is right-continuous with left limits almost surely.

We establish the relationship between regularity of a Hausdorff (LB)tv -space and its properties like (K), M.c.c., sequential completeness, local completeness. We give a sufficient and necessary condition for a Hausdorff (LB)tv-space to be an (LS)tv-space. A factorization theorem for (LN)tv-spaces with property (K) is also obtained.

The Gromov–Hausdorff distance between metric spaces appears to be a useful tool for modeling some object matching procedures. Since its conception it has been mainly used by pure mathematicians who are interested in the topology generated by this distance, and quantitative consequences of the definition are not very common. As a result, only few lower bounds for the distance are known, and the ...

Let (X; ) be a separable metric space and let (K(X); e ) denote the space of non-empty compact subsets of X with the Hausdor metric. The purpose of this paper is to investigate the relationship of the Hausdor dimension of a set E X to that of K(E) K(X).

Let A be a C *-algebra, T be a locally compact Hausdorff space equipped with a probability measure P and let (A t) t∈T be a continuous field of operators in A such that the function t → A t is norm continuous on T and the function t → A t is integrable. Then the following equality including Bouchner integrals holds T A t − T A s dP 2 dP = T |A t | 2 dP − T A t dP 2. (0.1) This equality is relat...

Last quarter, we introduced the closed diagonal condition for a prevariety to be a prevariety, and the “universally closed” condition for a variety to be complete. Earlier this quarter, we verified that in the case of complex prevarieties, these conditions are equivalent to the analytic topology being Hausdorff and compact, respectively. As we’ve discussed, in the scheme context a prevariety co...

A short proof of the fact that isomorphisms between algebras of smooth functions on Hausdorff smooth manifolds are implemented by diffeomorphisms is given. It is not required that manifolds are second countable or paracompact. This solves a problem stated by A. Wienstein. Some related results are discussed as well.