This is an announcement for the paper "An inequality for the entropy numbers and its application" by Vladimir Temlyakov. Abstract: We prove an inequality for the entropy numbers in terms of nonlinear Kolmogorov's widths. This inequality is in a spirit of known inequalities of this type and it is adjusted to the form convenient in applications for $m$-term approximations with respect to a given system. Also, we obtain upper bounds for the $m$-term approximation by the Weak Relaxed Greedy Algorithm with respect to a system which is not a dictionary. Archive classification: math.MG math.FA Submitted from: n.i.pentacaput@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.7624 or http://arXiv.org/abs/1301.7624