Exercise 10, § 2

General Topology, VI

Let $H_{n, p, q}$ denote the "quadric" in $\mathbf{R}^n$ defined by the equation

x_1^2 + x_1^2 + \cdots + x_p^2 - x_{p+1}^2 - \cdots - x_{p+q}^2 = 1 \quad (p + q \leq n).

Show that

H_{n, p, q}

is homeomorphic to

S_{p-1} \times \mathbf{R}^{n-p}

Solution

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