Nearness relations and topology
نویسنده
چکیده
J. Dobrakovová and the author in [7] introduced the relation of nearness in Banach space. In this paper we will go on investigating the nearness relation in a linear space with a countable vector base, focusing the results to topological properties of such relations.
منابع مشابه
Uniformities 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 کاملNearness Rules and Scaled Proximity (Extended Version)
An artificial intelligence system that processes geo-thematic data would profit from a (semi-)formal or controlled natural language interface that incorporates concepts for nearness. Though there already exists logical-engineering approaches giving sufficient conditions for nearness relations, we show within a logical analysis that these suffer from some deficiencies. Non-engineering approaches...
متن کاملDevelopable Spaces and Nearness Structures
Necessary and sufficient conditions on a nearness structure are provided for which the underlying topology is developable. It is also shown that a topology is developable if and only if it admits a compatible nearness structure with a countable base. Finally it is shown that a topological space is embeddable in a complete Moore space if and only if it admits a compatible nearness structure sati...
متن کاملShaping space: the possible and the attainable in RNA genotype-phenotype mapping.
Understanding which phenotypes are accessible from which genotypes is fundamental for understanding the evolutionary process. This notion of accessibility can be used to define a relation of nearness among phenotypes, independently of their similarity. Because of neutrality, phenotypes denote equivalence classes of genotypes. The definition of neighborhood relations among phenotypes relies, the...
متن کاملNearness of Visual Objects. Application of Rough Sets in Proximity Spaces
The problem considered in this paper is how to describe and compare visual objects. The solution to this problem stems from a consideration of nearness relations in two different forms of Efremovic̆ proximity spaces. In this paper, the visual objects are picture elements in digital images. In particular, this problem is solved in terms of the application of rough sets in proximity spaces. The ba...
متن کامل