second countability is hereditary

Suppose X is a second countable topological spaceMathworldPlanetmath and A is a subset in X. Then A (when equipped with the subspace topology) is also second countable.

Title second countability is hereditary
Canonical name SecondCountabilityIsHereditary
Date of creation 2013-03-22 15:22:45
Last modified on 2013-03-22 15:22:45
Owner matte (1858)
Last modified by matte (1858)
Numerical id 4
Author matte (1858)
Entry type Theorem
Classification msc 54D70