# intuition on the countable dense subset implying separability [duplicate]

Are there any good intuitions to understand why countable dense subset implies separability? Is the separability related to the opposite of connectedness? In Munkres, I am a bit confused after he mentioned that this is an unfortunate choice of terminology.

• It's the definition of separability that there is a countable dense subset. It's unfortunate terminology because separability has nothing to do with separation (or connectedness). – Daniel Fischer Aug 18 '14 at 21:09
• The reason it's unfortunate is that there are a large suite of so-callled separation axioms that talk about separating points/closed sets, and then there's suite of axioms that mandate various things be countable. separability is a countability axiom, not a separation axiom – JHance Aug 18 '14 at 21:10