In
topology, a
second-countable space, also called a
completely separable space, is a
topological space satisfying the
second axiom of countability. A space is said to be second-countable if its topology has a
countable base. More explicitly, this means that a topological space
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=2209)
is second countable if there exists some countable collection
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=409)
of open subsets of
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=2209)
such that any open subset of
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=2209)
can be written as a union of elements of some subfamily of
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=1205)
. Like other countability axioms, the property of being second-countable restricts the number of
open sets that a space can have.