منابع مشابه
Nonstandard Analysis in Point
We present Nonstandard Analysis by three axioms: the Extension, Transfer and Saturation Principles in the framework of the superstructure of a given innnite set. We also present several applications of this axiomatic approach to point-set topology. Some of the topological topics such as the Hewitt realcompactiication and the nonstandard characterization of the sober spaces seem to be new in the...
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Let (X,T ) be a topological space, and X a non–standard extension of X . There is a natural “standard” topology T on X generated by G, where G ∈ T . The topological space ( X, T ) will be used to study, in a systematic way, compactifications of (X,T ) . Mathematics Subject Classification: 031105, 54J05, 54D35, 54D60.
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Recently, Dag Normann and the author have established a connection between higher-order computability theory and Nonstandard Analysis; new results in both fields are obtained by exploiting this connection ([28]). Now, on the side of computability theory, the technique known as Grilliot’s trick constitutes a template for explicitly defining the Turing jump functional (∃) in terms of a given effe...
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Intuitively, it is tempting to view a cube in R as a discrete lattice with infinitesimal edges. A similar infinitesimal picture suggests itself with other fractal spaces such as the Sierpinski gasket or the Sierpinski sponge (see [13], [5].) The purpose of this paper is to show certain classes of metric spaces characterized by volume growth properties of balls ([4],[2]) can viewed as graphs wit...
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There is an ancient philosphical-religious divide over questions of infinity. This divide extends over mathematics and we see it in many forms. A perfect example is offered by the twin approaches to analysis: limits and infinitesimals. With Robinson’s discovery of nonstandard analysis, both approaches have achieved legitimacy. Today, there is a new approach, non-nonstandard analysis, which, in ...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1994
ISSN: 0168-0072
DOI: 10.1016/0168-0072(94)90023-x