Abstract
In the present paper we prove a criterion of Lipk-paracompactness for infinitedimensional manifold M modeled in nonnormable topological vector Fréchet space F. We establish that a manifold is Lipk-paracompact if and only if the model space F is paracompact and Lipk-normal. We prove a sufficient condition for existence of Lipk-partition of a unity on a manifold of class Lipk.
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Original Russian Text © Z.D. Al Nafie, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 10, pp. 8–14.
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Al Nafie, Z.D. Partition of a unity on infinite-dimensional manifold of the Lipschiz class Lipk . Russ Math. 61, 5–10 (2017). https://doi.org/10.3103/S1066369X17100024
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DOI: https://doi.org/10.3103/S1066369X17100024