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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.)
##### Keywords:
partition of unity; Lipschitz functions