Abstract
By the construction C<sup>Lipk</sup>(Ω) we mean the space of all continuous complex-valued functions of class Lip<sup>k</sup>, defined on an open subset Ω of Euclidean space ℝ<sup>n</sup> the present work, proved the paracompactness of the space C<sup>Lipk</sup>(Ω), also many important results were discussed and proved.
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