# second countability is hereditary

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

Title second countability is hereditary SecondCountabilityIsHereditary 2013-03-22 15:22:45 2013-03-22 15:22:45 matte (1858) matte (1858) 4 matte (1858) Theorem msc 54D70