Symmetric space

Definition
A topological space $$X$$ is termed symmetric if it satisfies the following equivalent conditions:


 * 1) Its defining ingredient::Kolmogorov quotient is a defining ingredient::T1 space.
 * 2) There is no subspace of the space that is a defining ingredient::Sierpinski space with the subspace topology.
 * 3) Given any two defining ingredient::topologically distinguishable points $$a,b \in X$$, there exists an open subset $$U$$ of $$X$$ such that $$a \in U, b \notin U$$.
 * 4) given points $$a,b \in X$$, the following are equivalent:
 * 5) * There exists an open subset of $$X$$ containing $$a$$ but not $$b$$
 * 6) * There exists an open subset of $$X$$ containing $$b$$ but not $$a$$