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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2006 • Question 3

Question

Math 6510 • Differentiable Manifolds Fall 2006 • Question 3

Let \(X,Y\subset \mathbb {R}^3\) be two 1-dimensional submanifolds. Show that there is \(v\in \mathbb {R}^3\) such that \(X\) is disjoint from \(Y+v:=\{y+v\mid y\in Y\}\).

Raw LaTeX

Let \(X,Y\subset\mathbb{R}^3\) be two 1-dimensional submanifolds. Show that there is
\(v\in\mathbb{R}^3\) such that \(X\) is disjoint from
\(Y+v:=\{y+v\mid y\in Y\}\).

Topic Tags

Smooth Manifolds and Embedded Submanifolds