Definition:Totally Separated Space

Definition

Definition 1

A topological space $T = \struct {S, \tau}$ is totally separated if and only if:

For every $x, y \in S: x \ne y$ there exists a separation $U \mid V$ of $T$ such that $x \in U, y \in V$.

Definition 2

A topological space $T = \struct {S, \tau}$ is totally separated if and only if each of its quasicomponents is a singleton set.

Also see

• Equivalence of Definitions of Totally Separated Space

• Results about totally separated spaces can be found here.