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Open cover of a metric space admits \(\ell_{\infty}\)-partition of unity. (English) Zbl 0537.54019
Summary: The result stated in the title has been already proved independently by Z. Frolík and J. Pelant. Our aim is to give an easy proof.

MSC:
54E35 Metric spaces, metrizability
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
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