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binormality; Luzin-Menchoff property; Banach space; weak topology
We study binormality, a separation property of spaces endowed with two topologies known in the real analysis as the Luzin-Menchoff property. The main object of our interest are Banach spaces with their norm and weak topologies. We show that every separable Banach space is binormal and the space $\ell^{\infty}$ is not binormal.
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