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retract
▪ I. † reˈtract, n. Obs. [f. the verb, or ad. med.L. retractus.] 1. Retractation (of errors, statements, etc.).1553 Eden Treat. Newe Ind. (Arb.) 10 He wrytte also a Booke of retractes in whych he correcteth hys owne errours. 1584 [R. Parsons] Leicester's Commonw. (1641) 29 For this cause hee hath hi... Oxford English Dictionary
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Retract (group theory)
Every direct factor is a retract. Conversely, any retract which is a normal subgroup is a direct factor. Every retract has the congruence extension property. Every regular factor, and in particular, every free factor, is a retract. wikipedia.org
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retract
retract/rɪˈtrækt; rɪ`trækt/ v[I, Tn](fml 文)1 withdraw (a statement, charge, etc) 撤回或撤消（声明、 指控等） The accused refused to retract (his statement). 那被告拒不撤消（其供述）.2 refuse to honour or keep (an agreement, etc) 拒绝执行或遵守（协议等） retract a promise, an offer, etc 食言、 撤消提议.3 move or pull (sth) back or in 缩回或拉回（某物）... 牛津英汉双解词典
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Testicles Retract Into Body (Move Inward) While Ejaculating
The reason why the testicle is pulled back into the body is because of an overactive muscle. The cremaster muscle is the one on which the testicle rests and if it contracts with an increased amount of force then the testicle may be pulled back up towards the abdomen.
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how to retract email in outlook
Feb 27, 2023 — If the recall is successful, you'll receive a notification. If the recall is unsuccessful, you'll receive a notification that tells you whether ...
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Homotopic retract vs deformation retract Let's say that $A \subset X$ is a deformation retract. It follows that $A$ is both a retract and a space homotopically equivalent to $X$. Is the converse true? Probably not, bu...
No. Let $X = \\{0,1,2,3,\dots\\}$ and $A = \\{1,2,3,\dots\\}$, both with the discrete topology, and let $i: A \to X$ be the inclusion. Then $i$ has a retraction $r: X \to A, n\mapsto\max\\{n,1\\}$, and is even a cofibration. $X$ and $A$ are clearly isomorphic. The inclusion, however, is not a homoto...
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Can any category be imbedded in a balanced category? It is a simple fact that any retract is an epimorphism, and that in a sub-category a retract preserves its epic property (the same for co-retract and monomorphism)....
Every presheaf category is balanced, so the Yoneda embedding does the job.
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If $X$ and $Y$ are subspaces of $Z$, $X \cong Y$ and $X$ is a retract of $Z$, is $Y$ also a retract of $Z$? If $X$ and $Y$ are subspaces of $Z$, $X \cong Y$ and $X$ is a retract of $Z$, is $Y$ also a retract of $Z$? ...
Then pick any spaces $Y\subseteq Z_0$ such that $Y$ is NOT a retract of $Z_0$. But $X$ is a retract of $Z$: define the retraction as the identity on $X$ (obviously).
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Deformation retract and homotopy equivalence If $A\subset X$ is a deformation retract of $X$. Are $X$ and $A$ homotopy equivalent?
The weaker form states that $A \subseteq X$ is a (weak)deformation retract of $X$ iff there's a map $r \colon X \to A$ such that $r$ is both a left and The stronger form states that $A$ is a deformation retract of $X$ iff exists a map $D \colon X \times I \to X$ such that $D(a,t)=a$ for every $a \in A$
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shall retract the licensing of its business - Reverso Context
Translations in context of "shall retract the licensing of its business" in English-Chinese from Reverso Context: If the case is serious, a security regulatory body shall retract the licensing of its business.
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Union and intersection of deformation retracts Let $X$ be a topological space and $A,B,\tilde{A}, \tilde{B}\subset X$. Is it true in general that if $A$ is a deformation retract of $\tilde{A}$ and $B$ is a deformati...
A circle does not deform retract onto the union of two points. So $\tilde A \cap \tilde B$ does not deform retract on $A \cap B$.
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Example Of A Non-Existent Retract I am looking for an example that disproves the claim that given any subspace $A$ of a topological space $X$, there exists a retract of $X$ onto $A$.
Here's the simplest possible example: Consider the space $X$ with three points $a,b,c$ and open sets $$\emptyset, \\{a\\},\\{c\\}, \\{a,c\\}, \\{a,b,c\\}.$$ Let $A=\\{a,c\\}$. There are only two maps from $X$ to $A$ which are the identity on $A$, and neither is continuous. E.g. if we send $b$ to $a$...
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If $A$ is a retract of $X$, then is the (reduced) suspension $SA$ a retract of $SX$? I have a compact Hausdorff space $X$ and $A$ a closed subset. Suppose $A$ is a retract of $X$, that is, there is a continuous map $r...
Both $S$ and $\Sigma$ are functors, so both preserve retracts: given maps $i: A \to X$ and $r: X \to A$ such that $r \circ i = 1_A$, then applying any functor $F$ gives $F(r) \circ F(i) = F(1_A) = 1_{F(A)}$.
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$A\times Y$ is retract of $X\times Y$ iff $A$ is retract of $X$ I have the following problem that I am stuck on. > Let $A$ be a subspace of $X$ and let $Y$ be a non-empty topological space. Show that $A\times Y$ is ...
Suppose $A\times Y$ is a retract of $X\times Y$. Conversely, suppose $A$ is a retract of $X$. Then there exists a retraction $r:X\to A$.
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Retract subspace of metric space is closed Let $(X,\varrho)$ be a metric space, and $Y\subseteq{X}$ a retract subspace of $X$. Show that $Y$ is closed in $X$.
Since $A$ is a retract subspace, there is a continuous map $r:X\to A$ such that $r(a)=a$ for every $a\in A$.
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