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The well-known completions of T 2 Cauchy spaces and T 2 filter spaces are extended to the completions of non-T 2 filter spaces, and a completion functor on the category of all filter spaces is described.
This is a preliminary report on the continuous action of convergence groups on convergence spaces. In particular , the convergence structure on the homeomorphism group and its continuous action are investigated in this paper. Also, attempts have been made to establish a one-to-one correspondence between continuous action of a convergence group and its… (More)