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Nonstandard methods in large-scale topology [PDF]
Topology and its Applications, 2019 Accepted by Topology and its Applications; corrigendum ...
Takuma Imamura
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Nonstandard analysis in topology: nonstandard and standard compactifications [PDF]
Journal of Symbolic Logic, 2000 AbstractLet (X, T) be a topological space and *X a nonstandard extension of X. Sets of the form *G. where G ∈ T, form a base for the “standard” topology ST on *X. The topological space (*X, ST) will be used to study compactifications of (X, T) in a systematic way.
Salbany, S., Todorov, Todor D.
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Nonstandard topology on function spaces with applications to hyperspaces [PDF]
Transactions of the American Mathematical Society, 1993 In this paper the techniques of Nonstandard Analysis are used to study topologies on the set of all continuous functions. We obtain nonstandard characterizations for conjoining and splitting topologies and we give a complete description of the monads of the compact-open topology which leads to very elegant and simple proofs of some important results ...
H. Render
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由度量空间诱导的*-拓扑和s-拓扑(* -Topology and s-topology induced by metric space)
Zhejiang Daxue xuebao. Lixue ban, 2018 This paper studies * -topology and s-topology in polysaturated nonstandard model,which are induced by metric space on two nonstandard sets. In order to construct * -topology , the set of finite points is introduced.
SHIYanwei(史艳维) +1 more
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SPθ-TOPOLOGICAL GROUPS IN NONSTANDARD ANALYSIS
Assiut University Journal of Multidisciplinary Scientific Research, 2016 In 1982, Mashhour et al [1], defined a new version of nearly open sets, which is a significant notion to the field of general topology, which are called preopen sets.
I. Hamad, T. Ismail, Sami A. Hussein
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Coarse Topologies in Nonstandard Extensions via Separative ultrafilters [PDF]
Illinois Journal of Mathematics, 1983 *As far as we know, it is an open question whether *X can be To when X is infinite and * is Ol-saturated. However, with the help of extra set theory (notably Martin’s Axiom (MA) and the Continuum Hypothesis (CH)), we can construct extensions * in which *X can be To (even Tichonov) for a large class of spaces X.
Bankston, Paul
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Fuzzy-Logic-Controlled Hybrid Active Filter for Matrix Converter Input Current Harmonics
Energies, 2022 The proliferation of matrix converter interfaces coupled with traditional loads produces nonstandard and high-frequency harmonics in the range of (2 to 150) kHz in the power system.
Asare Koduah, Francis Boafo Effah
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International Transactions on Electrical Energy Systems, 2022 Vector control of an asynchronous machine is traditionally accomplished by analogizing it to a separately excited DC machine. It provides decoupled torque and flux control that is perpendicular to each other, ensuring that neither vector interferes with ...
Belqasem Aljafari +3 more
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An Expository on Some Nonstandard Compactifications
Advances in Pure Mathematics, 2021 Three classical compactification procedures are presented with nonstandard flavour. This is to illustrate the applicability of Nonstandard analytic tool to beginners interested in Nonstandard analytic methods.
Alagu S. Somasundaram, R. Kala
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The nonstandard theory of topological vector spaces [PDF]
Transactions of the American Mathematical Society, 1972 In this paper the nonstandard theory of topological vector spaces is developed, with three main objectives: (1) creation of the basic nonstandard concepts and tools; (2) use of these tools to give nonstandard treatments of some major standard theorems; (3) construction of the nonstandard hull of an arbitrary topological vector space, and the beginning ...
Henson, C. Ward, Moore, L. C. jun.
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