Definition:Totally Separated Space/Definition 1
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Definition
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 $x \in U, y \in V$.
Also see
- Results about totally separated spaces can be found here.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $4$: Connectedness: Disconnectedness