If X is a quasitopological space -Spanier space in this paper-, a topological space q X can be associated to X. A subset F of X is called closed if it is closed in q X. Interesting properties of the closed subspaces of a quasitopological space are examined.
Let P be a small category and A(B) a category such that the functor A → A (B → B) determined by the projection functor A x P → A (B x P → B) has an adjoint for all small category P. A functor G: B → A has an adjoint functor if and only if it has and adjoint functor "via" evaluation. If Q is another small category and F: P → Q an arbitrary functor, the functor A: A → A has an adjoint functor.
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