Abstract
Let (X, V, W) be a bitopological space. The topology V is a (fine) cotopology of W if V ⊂ W, V is a T1-topology and W is (completely) regular with respect to V.Let (X, V, W) be a bitopological space such that V is a fine cotopology of W. Related to special closed subbases S and T of V and W respectively, a construction of a pairwise dense embedding e: (X, V, W) → (X, V, W) is presented such that V is a compact fine cotopology of W.The main properties of our construction are the following.1.(1) If the topology W is compact, then V = W and (X, W) is a Wallman-type compactification of (X, W). Every Wallman-type compactification can be reproduced in this way.2.(2) If the topology W̄ is metrizable, then (X, W) is a topologically complete extension of (X, W). Every topologically complete metrizable extension can be reproduced by this construction.
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