منابع مشابه
Weak Bases and Metrization
Several weak base (in the sense of A. V. Arhangel'skiT) metrization theorems are established, including a weak base generalization of the Nagata-Smirnov Metrization Theorem.
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It is shown that certain weak-base structures on a topological space give a D-space. This solves the question by A.V. Arhangel’skii of when quotient images of metric spaces are D-spaces. A related result about symmetrizable spaces also answers a question of Arhangel’skii. Theorem. Any symmetrizable space X is a D-space (hereditarily). Hence, quotient mappings, with compact fibers, from metric s...
متن کاملNagata-Smirnov Metrization Theorem.nb
Introduction: The Nagata-Smirnov Metrization theorem gives a full characterization of metrizable topological spaces. In other words, the theorem describes the necessary and sufficient conditions for a topology on a space to be defined using some metric. As a motivational example, consider the discrete topology on some space (every subset of the space is open). Though it might not be apparent to...
متن کاملIonization of Water, Weak Acids and Weak Bases
lthough many of the solvent properties of water can be explained in terms of the uncharged H2O molecules,the small degree of ionization of water to hydrogen ions (H) and hydroxide ions (OH ) must also be taken into account. Like all reversible reactions, the ionization of water can be described by an equilibrium constant. When weak acids or weak bases are dissolved in water, they can contribute...
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We present an algorithm that, given a channel, determines if there is a distance for it such that the maximum likelihood decoder coincides with the minimum distance decoder. We also show that any metric, up to a decoding equivalence, can be isometrically embedded into the hypercube with the Hamming metric, and thus, in terms of decoding, the Hamming metric is universal. keywords: Coding Theory;...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1976
ISSN: 0002-9947
DOI: 10.2307/1997674