Some Properties Preserved by Weak Nearness
نویسنده
چکیده
We show that the properties of being injective, surjective, continuous, strongly surjective, stably solvable, carry over to weakly-near maps. We also prove a data dependence theorem for equations of the form A(x) = z, where A is weakly-near to some bijective map.
منابع مشابه
Near semigroups on nearness approximation spaces
In this paper, our approach is to study properties of approximations on nearness approximation spaces. Afterwards, our aim is to define near semigroups and near ideals on near approximation spaces. We introduce some properties of these near structures. The nearness of sets and, in particular, the nearness of algebraic structures on nearness approximation spaces fits within the milieu of fuzzy s...
متن کاملMatrix Nearness Problems and Applications ∗
A matrix nearness problem consists of finding, for an arbitrary matrix A, a nearest member of some given class of matrices, where distance is measured in a matrix norm. A survey of nearness problems is given, with particular emphasis on the fundamental properties of symmetry, positive definiteness, orthogonality, normality, rank-deficiency and instability. Theoretical results and computational ...
متن کاملComputational Structure in Three-Valued Nearness Relations
The development of cognitively plausible models of human spatial reasoning may ultimately result in computational systems that are better equipped to meet human needs. This paper explores how human subjects perceive the qualitative spatial relation nearness within an environmental space. Based on experimental data, a three-valued nearness relation is analysed in two stages. First, the results a...
متن کاملOn categories of merotopic, nearness, and filter algebras
We study algebraic properties of categories of Merotopic, Nearness, and Filter Algebras. We show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. The forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the cat...
متن کاملUniformities and covering properties for partial frames (I)
Partial frames provide a rich context in which to do pointfree structured and unstructured topology. A small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. These axioms are sufficiently general to include as examples bounded distributive...
متن کامل