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Abstract. In this paper the author studies properties of d- regular mappings connected with the tasks of continuous mappings extension. Results described in this article are directly related to extension theory developed in A. N. Dranishnikov’s, E. V. Shchepin’s works. The solution of a number of problems put forward by extension theory in this paper organically supplements this theory giving it integrity and diversity. In particular, the article gives a characterization of absolute retracts in the language of topologies extension operators. The proof of the main results of this paper is based on the use of modern mathematical methods.
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Key words and phrases: топологическое пространство, непрерывное отображение, тихоновский куб, компакт, ретракт, экстремально несвязное пространство, topological space, continuous mapping, Tychonov cube, compact, retract, extremely disconnected space
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