Nagata-Smirnov Metrization Theorem.nb
نویسنده
چکیده
Introduction: The Nagata-Smirnov Metrization theorem gives a full characterization of metrizable topological spaces. In other words, the theorem describes the necessary and sufficient conditions for a topology on a space to be defined using some metric. As a motivational example, consider the discrete topology on some space (every subset of the space is open). Though it might not be apparent to the untrained observer, this topology is actually defined by the following 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.
متن کاملWeak Bases and Metrization
Several weak base (in the sense of A. V. Arhangel'skiT) metrization theorems are established, including a weak base generalization of the Nagata-Smirnov Metrization Theorem.
متن کاملThe Nagata - Smirnov Theorem . Part I 1
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 cond...
متن کاملThe Quasimetrization Problem in the (Bi)topological Spaces
It is our main purpose in this paper to approach the quasi-pseudometrization problem in (bi)topological spaces in a way which generalizes all the well-known results on the subject naturally, and which is close to a " Bing-Nagata-Smirnov style " characterization of quasi-pseudometrizability. under the Creative Commons Attribution License, which permits unrestricted use, distribution , and reprod...
متن کامل