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Manifolds are [[Hausdorff space|Hausdorff]] and [[2nd-countable space|2nd-countable]].
Manifolds are [[Hausdorff space|Hausdorff]] and [[2nd-countable space|2nd-countable]].
Example: Consider the set of points <math>[x_0:x_1:x_2]</math>, where <math>x_i</math> are not all zero, and where we declare <math>[x_0:x_1:x_2]</math> to be equivalent to <math>[y_0:y_1:y_2]</math> if <math>x_i = \lambda y_i</math>. This space describes the set <math>\mathbf{R}P^2</math> of all one-dimensional subspaces of <math>R^3</math>.
[[Category:Mathematics]]
[[Category:Mathematics]]
[[category: Topology]]
[[category: Topology]]