Abstract
We prove that any product of quotient maps in the category of quasi-uniform spaces and quasi-uniformly continuous maps is a quotient map. We also show that a quasi-uniformly continuous map from a product of quasi-uniform spaces into a quasi-pseudometric T 0 -space depends on countably many coordinates. Furthermore we characterize those quasi-uniformities that are unique in their quasi-proximity class and prove that this property is preserved under arbitrary products in the category of quasi-uniform spaces.
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