Uncountable group of continuous transformations of unit segment preserving tails of Q_2-representation of numbers
| Autor: | Mykola Pratsiovytyi, Sofiia Ratushniak, Lysenko Iryna |
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| Jazyk: | English<br />Ukrainian |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Pracì Mìžnarodnogo Geometričnogo Centru, Vol 17, Iss 2, Pp 133-142 (2024) |
| Druh dokumentu: | article |
| ISSN: | 2072-9812 2409-8906 |
| DOI: | 10.15673/pigc.v17i2.2755 |
| Popis: | We consider two-base Q2-representation of numbers of segment [0;1] which is defined by two bases q0 ∈ (0;1), q1 = 1-q0 and alphabet A={0,1}, (αn) ∈ A × A × .... It is a generalization of classic binary representation q0=1/2. In the article we prove that the set of all continuous bijections of segment [0;1] preserving "tails" of Q2-representation of numbers forms an uncountable non-abelian group with respect to composition such that it is a subgroup of the group of continuous transformations preserving frequencies of digits of Q2-representation of numbers. Construction of such transformations (bijections) is based on the left and right shift operators for digits of Q2-representation of numbers. |
| Databáze: | Directory of Open Access Journals |
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