Exercise 11, § 3

General Topology, VI, p. 27

In the projective space $P_n$ let $C_{n,p}$ be the “second degree cone” defined by the equation

x_1^2 + x_2^2 + \cdots + x_p^2 - x_{p+1}^2 - \cdots - x_n^2 = 0 \quad (1 \leq p \leq n-1).

Now prove that the complement of

\{0\}

C_{n,p}

is homeomorphic to

\mathbf{R} \times H_{n-1,p}

(with the notation of Exerc. 10).

Solution

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