a quasiorder being defined as reflexive and transitive - not antisymmetric (if also antisymmetric then it is a partial ordering).
it is a trivial quasiorder iff: (Ax,y)(x<=y). can someone provide me with a few canonical, if not pathological, examples of a trivial quasiorder?
what is the relation between a neighborhood and an open set? a specialisation quasiorder .=. (x<=y) iff every neighborhood of x is a neighborhood of y. i need a few examples of a specialisation quasiorder.
why is a singleton necessarily a closed set -- why can't it be declared open?