topologically transitive

A continuous surjection $f$ on a topological space $X$ to itselfis topologically transitive if for everypair of open sets $U$ and $V$ in $X$ there is an integer $n>0$ such that $f^{n}(U)\\cap V\eq\\emptyset$ , where $f^{n}$ denotes the $n$ -th iterate of $f$ .

If for every pair of open sets $U$ and $V$ there is an integer $N$ such that $f^{n}(U)\\cap V\eq\\emptyset$ for each $n>N$ , we say that $f$ is topologically mixing.

If $X$ is a compact metric space, then $f$ is topologically transitive if and only if there exists a point $x\\in X$ with a dense orbit, i.e. such that $\\mathcal{O}(x,f)=\\{f^{n}(x):n\\in\\mathbb{N}\\}$ is dense in $X$ .

单词	TopologicallyTransitive
释义	topologically transitive A continuous surjection $f$ on a topological space $X$ to itselfis topologically transitive if for everypair of open sets $U$ and $V$ in $X$ there is an integer $n>0$ such that $f^{n}(U)\\cap V\eq\\emptyset$ , where $f^{n}$ denotes the $n$ -th iterate of $f$ . If for every pair of open sets $U$ and $V$ there is an integer $N$ such that $f^{n}(U)\\cap V\eq\\emptyset$ for each $n>N$ , we say that $f$ is topologically mixing. If $X$ is a compact metric space, then $f$ is topologically transitive if and only if there exists a point $x\\in X$ with a dense orbit, i.e. such that $\\mathcal{O}(x,f)=\\{f^{n}(x):n\\in\\mathbb{N}\\}$ is dense in $X$ .
随便看	GroupActionsAndHomomorphisms group actions and homomorphisms GroupCalgebra group C^*-algebra GroupCohomology group cohomology GroupCohomologytopologicalDefinition group cohomology (topological definition) GroupExtension group extension GroupHomomorphism group homomorphism GroupingMethodForFactoringPolynomials grouping method for factoring polynomials GroupInverse group inverse GrouplikeElements grouplike elements GrouplikeElementsInHopfAlgebras grouplike elements in Hopf algebras GroupOfUnits group of units Groupoid groupoid GroupoidAction