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We observe that the well-monotone (open covering) quasiuniformity of each topological space is left K-complete. On the other hand, we exhibit an example of a topological space the fine quasiuniformity of which is not D-complete. The semicontinuous quasiuniformity of a countably metacompact space X is shown to be D-complete if and only if X is closed-complete. Moreover it is proved that the well-monotone quasiuniformity of a ccc regular space X is D-complete if and only if X is almostdoi:10.1016/s0166-8641(96)00044-2 fatcat:fwngienyirgz7otv4lmuxsmqgy