Tkachuk, V. V. A short proof of a classical result of M. G. Tkachenko. (English) Zbl 1083.54017 Topol. Proc. 26(2001-2002), No. 2, 851-856 (2002). Summary: We give a comparatively short proof of a theorem which states that any compact space that is a continuous image of a dense subspace of a \(\Sigma\)-product of spaces with countable network, is metrizable. This is a very deep and non-trivial result of M.G. Tkachenko obtained in 1982. The original proof consists of eight pages of a very compressed text which involves construction of an inverse system whose elements are also constructed using additonal inverse systems. We give a transparent proof on less than three pages hoping to contribute to a better understanding of the features of dense subspaces of \(\Sigma\)-products responsible for metrizability of their compact continuous images. Cited in 1 Document MSC: 54E35 Metric spaces, metrizability 54C05 Continuous maps 54D30 Compactness Keywords:cosmic space; pointwise countable type; compact space; continuous image; dense subspace of a \(\Sigma\)-product PDFBibTeX XMLCite \textit{V. V. Tkachuk}, Topol. Proc. 26(2001--2002), No. 2, 851--856 (2002; Zbl 1083.54017)