Category:Definitions/Separations

This category contains definitions related to separations in the context of topology.
Related results can be found in Category:Separations.

Let $T = \struct {S, \tau}$ be a topological space.

Let $A$ and $B$ be open sets of $T$.

$A$ and $B$ form a separation of $T$ if and only if:

$(1): \quad A$ and $B$ are non-empty

$(2): \quad A \cup B = S$

$(3): \quad A \cap B = \O$