Displaying similar documents to “Extensions of Ćirić generalised contractions”

Compactification-like extensions

M. R. Koushesh

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Let X be a space. A space Y is called an extension of X if Y contains X as a dense subspace. For an extension Y of X the subspace Y∖X of Y is called the remainder of Y. Two extensions of X are said to be equivalent if there is a homeomorphism between them which fixes X pointwise. For two (equivalence classes of) extensions Y and Y' of X let Y ≤ Y' if there is a continuous mapping of Y' into Y which fixes X pointwise. Let 𝓟 be a topological property. An extension Y of X is called a 𝓟-extension...

Definable quantifiers in second order arithmetic and elementary extensions of ω-models

Wojciech Guzicki

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CONTENTS0. Introduction and terminology..............................................................51. Quantifiers and elementary extensions..............................................82. Elementary extensions of countable models of set theory................153. Interpretations of set theory in extensions of A₂...............................214. Definable quantifiers in models of A₂...............................................325. Elementary generic extensions........................................................40References..........................................................................................50 ...

Split extensions and semidirect products of unitary magmas

Marino Gran, George Janelidze, Manuela Sobral (2019)

Commentationes Mathematicae Universitatis Carolinae

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We develop a theory of split extensions of unitary magmas, which includes defining such extensions and describing them via suitably defined semidirect product, yielding an equivalence between the categories of split extensions and of (suitably defined) actions of unitary magmas on unitary magmas. The class of split extensions is pullback stable but not closed under composition. We introduce two subclasses of it that have both of these properties.