Of course every finite topological space is Alexandroff, but there are also bigger Alexandroff spaces. For example let denote the set of real numbers and let . Then is a topology on and is an Alexandroff space.
If is an Alexandroff space and , then we may talk about smallest open neighbourhood of . Indeed, let
Then is open.
|Date of creation||2013-03-22 18:45:41|
|Last modified on||2013-03-22 18:45:41|
|Last modified by||joking (16130)|