A Characterization of Order Topologies by Means of Minimal 7vtopologies
نویسندگان
چکیده
In this article we give a purely topological characterization for a topology 3 on a set X to be the order topology with respect to some linear order R on X, as follows. A topology 3 on a set X is an order topology iff (X, 3) is a TVspace and 3 is the least upper bound of two minimal 7Vtopologies [Theorem 1 ]. From this we deduce a purely topological description of the usual topology on the set of all real numbers. That is, a topological space (X, 3) is homeomorphic to the reals with the usual topology iff (X, 3) is a connected, separable, 7Vspace, and 3 is the least upper bound of two noncompact minimal TVtopologies [Theorem 2].
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