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**nweissma** 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?

thanks.