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...s (inverses of collapses), and a homotopy equivalence is a simple homotopy equivalence if it is homotopic to such a map. The obstruction to a homotopy equivalence being a simple homotopy equivalence is the [[Whitehead torsion]], <math>\tau(f).</math> ...

{{Short description|Statement about equivalence relations}} ...(1987), ISBN 0 444 87943 9.</ref> is a statement about [[Equivalence class|equivalence relations]], named after [[Jack Silver]].<ref name="YanfangThesis">L. Yanfa ...

{{Short description|Mathematical equivalence relation}} ...'''contact equivalence''', is an [[equivalence relation]] between [[germ (mathematics)|map germs]]. It was introduced by [[John Mather (mathematician)|John Math ...

{{Short description|Generalization of equivalence classes to scheme theory}} ...ation to [[category theory]], used in [[scheme theory]]|the common meaning|Equivalence class}} ...

'''S-equivalence''' is an [[equivalence relation]] on the families of [[Stable vector bundle|semistable]] [[vector ...emistable locally free ''E'' on ''X'' admits a Jordan-Hölder [[filtration (mathematics)|filtration]] with stable [[subquotient]]s, i.e. ...

In [[graph theory]], a branch of [[mathematics]], two graphs ''G'' and ''H'' are called '''homomorphically equivalent''' i Homomorphic equivalence also comes up in the theory of [[database]]s. Given a [[database schema]], ...

...h> is a map over ''B'' for ''t''.) It is a relative analog of a [[homotopy equivalence]] between spaces. ...D'' → ''B'', ''q'': ''E'' → ''B'', if ƒ: ''D'' → ''E'' is a fiber-homotopy equivalence, then for any ''b'' in ''B'' the restriction ...

{{Short description|Equivalence relation on mathematical measures}} In [[mathematics]], '''exponential equivalence of measures''' is how two sequences or families of [[probability measure]]s ...

...s. For every adequate equivalence relation, one may define the [[category (mathematics)|category]] of [[motive (algebraic geometry)|pure motives]] with respect to ...geometry)|divisor]]s modulo linear equivalence. All cycles modulo rational equivalence form the [[Chow ring]]. ...

...s theorem''' is a fundamental result on the [[equivalence (measure theory)|equivalence]] or [[singular measure|mutual singularity]] of countable [[product measure ...u</math> are equivalent, or else they are mutually singular. Furthermore, equivalence holds precisely when the infinite product ...

...'s trick''' is a method for giving a definition of equivalence classes for equivalence relations on a proper class (Jech 2003:65) by referring to levels of the [[ ...not on the [[axiom of choice]]. It can be used to define [[representative (mathematics)|representative]]s for [[ordinal number]]s in ZF, [[Zermelo–Fraenkel set th ...

...chapter = An efficient algorithm for branching bisimulation and stuttering equivalence | title = Proceedings of the 17th International Colloquium on Automata, Lan [[Image:Stuttering Equivalence.pdf|thumb|The paths <math>\pi</math> and <math>\pi'</math> are stuttering e ...

...ountable classes, that can, in a certain sense, be approximated by [[Borel equivalence relation]]s that have finite classes. ...rel set|Borel subsets]] (and forgetting the [[topology]]). Let ''E'' be an equivalence relation on ''X''. We will say that ''E'' is Borel if ''E'' is a Borel subs ...

In [[mathematics]], '''perfectoid spaces''' are [[adic space]]s of special kind, which occur ...ism]] Φ is [[surjective]] on ''K''°/''p'' where ''K''° denotes the [[ring (mathematics)|ring]] of power-bounded elements. ...

In mathematics, '''Giraud subcategories''' form an important class of subcategories of [[G ...thful functors|fully faithful]] and induces an [[equivalence of categories|equivalence]] between <math>\mathcal{A}/\mathcal{C}</math> and the Giraud subcategory < ...

In [[mathematics]], a '''weak equivalence''' is a notion from [[homotopy theory]] that in some sense identifies objec A model category is a [[category (mathematics)|category]] with classes of [[morphism]]s called weak equivalences, [[fibra ...

...braic equivalence, which are two important [[Adequate equivalence relation|equivalence relations]] of [[algebraic cycle]]s. ...|title=On the Periods of Certain Rational Integrals: I |journal=Annals of Mathematics |year=1969 |volume=90 |issue=3 |pages=460–495 }} ...

...capsulates various more specific concepts, such as that of a [[hyperfinite equivalence relation]], but is of interest in and of itself. ...>F</math> have a similar level of complexity. When one talks about [[Borel equivalence relation]]s and requires <math>f</math> to be Borel measurable, this is oft ...

...nce}}) is a mathematical [[Proof (mathematics)|proof]] technique where the equivalence of several statements can be proven without having to prove all pairwise eq ...pringer-Verlag |isbn=978-3-662-49870-5 |pages=28 |language=de |trans-title=Mathematics for Computer Scientists: Fundamentals and Applications}}</ref> ...

...es, an additional requirement is made that all operations must respect the equivalence between elements. For example, if <code>f</code> is a function on values of ...ke |editor-first=Edmund |editor2-last=Kozen |editor2-first=Dexter |chapter=Mathematics as programming |chapter-url=https://link.springer.com/chapter/10.1007/3-540 ...