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2017 A necessary and sufficient condition for coincidence with the weak topology
Joseph Clanin, Kristopher Lee
Involve 10(2): 257-261 (2017). DOI: 10.2140/involve.2017.10.257

Abstract

For a topological space X, it is a natural undertaking to compare its topology with the weak topology generated by a family of real-valued continuous functions on X. We present a necessary and sufficient condition for the coincidence of these topologies for an arbitrary family A C(X). As a corollary, we give a new proof of the fact that families of functions which separate points on a compact space induce topologies that coincide with the original topology.

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Joseph Clanin. Kristopher Lee. "A necessary and sufficient condition for coincidence with the weak topology." Involve 10 (2) 257 - 261, 2017. https://doi.org/10.2140/involve.2017.10.257

Information

Received: 10 September 2015; Revised: 9 December 2015; Accepted: 19 December 2015; Published: 2017
First available in Project Euclid: 13 December 2017

zbMATH: 1355.54021
MathSciNet: MR3574300
Digital Object Identifier: 10.2140/involve.2017.10.257

Subjects:
Primary: 46E25 , 54A10

Keywords: continuous functions , weak topology

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.10 • No. 2 • 2017
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