Editing Second-countable space (section)

===Other properties===

*A continuous, [[open map|open]] [[image (mathematics)|image]] of a second-countable space is second-countable.
*Every [[subspace (topology)|subspace]] of a second-countable space is second-countable.
*[[Quotient space (topology)|Quotients]] of second-countable spaces need not be second-countable; however, ''open'' quotients always are.
*Any countable [[product space|product]] of a second-countable space is second-countable, although uncountable products need not be.
*The topology of a second-countable T<sub>1</sub> space has [[cardinality]] less than or equal to ''c'' (the [[cardinality of the continuum]]).
*Any base for a second-countable space has a countable subfamily which is still a base.
*Every collection of disjoint open sets in a second-countable space is countable.