Geodesic
Partition of a unity on infinite-dimensional manifold of the Lipschitz class~$\mathrm{Lip}^k$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2017), pp. 8-14

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We prove a critrion of $\mathrm{Lip}^k$-paracompactness of infinite-dimensional manifold $M$ modeled in nonnormable topological Fréchet vector space $F$. We establish that for $\mathrm{Lip}^k$-paracompactness it is necessary and sufficcient for the space of models $F$ to be paracompact and $\mathrm{Lip}^k$-normal. We prove suffcient condition of existence of $\mathrm{Lip}^k$-partition of unity on a manifold of class $\mathrm{Lip}^k$.
Keywords: infinite-dimensional manifold, paracompactness, partition of unity, convenient topological vector spaces, nonnormable Fréchet spaces. 
@article{IVM_2017_10_a1,
     author = {Z. D. Al-Nafie},
     title = {Partition of a unity on infinite-dimensional manifold of the {Lipschitz} class~$\mathrm{Lip}^k$},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {8--14},
     publisher = {mathdoc},
     number = {10},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_10_a1/}
}
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Z. D. Al-Nafie. Partition of a unity on infinite-dimensional manifold of the Lipschitz class~$\mathrm{Lip}^k$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2017), pp. 8-14. http://geodesic.mathdoc.fr/item/IVM_2017_10_a1/