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Topogenous orders in the sense of Császár are a common generalization of proximity and topology. Cech closures are a generalization of the topological closure operators in the sense of Kuratowski. We show that the topogenous orders as well as the Cech closures are special cases of the so called compressed operators. Moreover, the now defined categoryCOM (in germanBAL) of compress spaces and compress faithful maps is a properly fibred topological category in the sense of Herrlich which is weakly cartesian closed, that means the product map of two quotient maps inCOM is a quotient map inCOM. Therefore by results of L. D. Nel it is possible to construct a cartesian closed properly fibred topological category in whichCOM can be nicely embedded. Further it turns out that the compressed operators be in a natural connexion with the uniform convergence structures in the sense of Cook and Fischer and in addition with the limit structures in the sense of Fischer. For principal ideal uniform convergence structures we prove that they are precompact and complete iff the properly constructed compressed operator is compact.