Monthly Archives: August 2010

(Least) upper bounds for order-preserving maps

A map between non-empty partially ordered sets is said to be order-preserving if entails . The collection of order-preserving maps can be endowed with an ordering relation in a natural way by setting in iff for all . When considering … Continue reading

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T_2 and compactness

Any compact (= Hausdorff) space   is on the brink of being compact and being : (1) If we endow with a topology distinct from such that , then is not compact any more; and (2) if we endow with … Continue reading

Posted in Point-set topology | Leave a comment