This note provides conditions under which Zadeh extension of a map between L -topological spaces preserves semicontinuity and continuity of functions with values in the L-unit interval. Invariance of complete L-regularity under continuous open–closed surjections is established among others. © 2012 Elsevier B.V. All rights reserved.

In the present paper we study the weak lower semicontinuity of the functional

We prove a semicontinuity theorem for an integral functional made up by a polyconvex energy and a surface term. Our result extends to the BV framework a well known result by John Ball.

This paper presents a partial solution to the long standing open problem of termination of one rule string rewriting Overlaps between the two sides of the rule play a central role in existing termination criteria We characterize termination of all one rule string rewriting systems that have one such overlap at either end This both completes a result of Kurth and generalizes a result of Shikishi...

Katětov-Tong insertion type theorem For every upper semicontinuous real function f and lower semicontinuous real function g satisfying f ≤ g, there exists a continuous real function h such that f ≤ h ≤ g (Katětov 1951, Tong 1952). For every lower semicontinuous real function f and upper semicontinuous real function g satisfying f ≤ g, there exists a continuous real function h such that f ≤ h ≤ ...

The concept of the lower limit for vector-valued mappings is the main focus of this work. We first introduce a new definition of adequate lower and upper level sets for vector-valued mappings and establish some of their topological and geometrical properties. Characterization of semicontinuity for vector-valued mappings is thereafter presented. Then, we define the concept of vector lower limit,...

In this paper we present a topology on the space of real-valued functions defined on a functionally Hausdorff space X that is finer than the topology of pointwise convergence and for which (1) the closure of the set of continuous functions C(X) is the set of upper semicontinuous functions on X , and (2) the pointwise convergence of a net in C(X) to an upper semicontinuous limit automatically en...

We study weak lower semicontinuity of integral functionals in W 1,p under standard p-growth conditions, with integrands whose negative part may have p-growth as well. MSC 2000: 49J45

Firms and organizations often need to collect and analyze sensitive consumer data. A common problem encountered in such evidence-based research is that they cannot collect all essential information from one sample, and may need to link non-overlapping data items across independent samples. We propose an automated nonparametric data fusion solution to this problem. The proposed methods are not r...