The Nagata - Smirnov Theorem . Part I 1
نویسنده
چکیده
In this paper we define a discrete subset family of a topological space and basis sigma locally finite and sigma discrete. First, we prove an auxiliary fact for discrete family and sigma locally finite and sigma discrete basis. We also show the necessary condition for the Nagata Smirnov theorem: every metrizable space is T3 and has a sigma locally finite basis. Also, we define a sufficient condition for a T3 topological space to be T4. We introduce the concept of pseudo metric.
منابع مشابه
Some Characterizations of Developable Spaces
Two characterizations of developable spaces are proved which may be viewed as analogues, for developable spaces, of the Nagata-Smirnov metrization theorem or of the "double sequence metrization theorem " of Nagata respectively.
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