immersion

Let $X$ and $Y$ be manifolds, and let $f$ be a mapping $f:X\\to Y$ . Choose $x\\in X$ , and let $y=f(x)$ . Recall that $df_{x}:T_{x}(X)\\to T_{y}(Y)$ is the derivative of $f$ at $x$ , and $T_{z}(Z)$ is the tangent space of manifold $Z$ at point $z$ .

If $df_{x}$ is injective, then $f$ is said to be an immersion at x. If $f$ is an immersion at every point, it is called an immersion.

If the image of $f$ is also closed, then $f$ is called a closed immersion.

The notion of closed immersion (http://planetmath.org/ClosedImmersion) for schemes is the analog of this notion in algebraic geometry.

单词	Immersion
释义	immersion Let $X$ and $Y$ be manifolds, and let $f$ be a mapping $f:X\\to Y$ . Choose $x\\in X$ , and let $y=f(x)$ . Recall that $df_{x}:T_{x}(X)\\to T_{y}(Y)$ is the derivative of $f$ at $x$ , and $T_{z}(Z)$ is the tangent space of manifold $Z$ at point $z$ . If $df_{x}$ is injective, then $f$ is said to be an immersion at x. If $f$ is an immersion at every point, it is called an immersion. If the image of $f$ is also closed, then $f$ is called a closed immersion. The notion of closed immersion (http://planetmath.org/ClosedImmersion) for schemes is the analog of this notion in algebraic geometry.
随便看	LineSegment line segment LineThroughAnIntersectionPoint line through an intersection point LinftyXmu LinkBetweenInfiniteProductsAndSums link between infinite products and sums LiouvilleApproximationTheorem Liouville approximation theorem LiouvilleFunction Liouville function LiouvilleNumber Liouville number LiouvillesTheorem LiouvillesTheorem1 Liouville’s theorem Liouville’s theorem LipschitzCondition Lipschitz condition LipschitzConditionAndDifferentiability Lipschitz condition and differentiability LipschitzConditionAndDifferentiabilityResult Lipschitz condition and differentiability result LipschitzFunction Lipschitz function