Let "S" be a subset of R"n". Observe first the following: if "a" is a limit point of "S", then any finite collection "C" of open sets, such that each open set "U" ∈ "C" is disjoint from some neighborhood "V""U" of "a", fails to be a cover of "S". Indeed, the intersection of the finite family of sets "V""U" is a neighborhood "W" of "a" in R"n". Since "a" is a limit point of "S", "W" must contain a point "x" in "S". This "x" ∈ "S" is not covered by the family "C", because every "U" in "C" is disjoint from "V""U" and hence disjoint from "W", which contains "x".