Generating subgroups of the circle using statistical convergence of order α

Autor:	Pratulananda Das, K. Bose, W. He
Rok vydání:	2020
Předmět:	General Mathematics 010102 general mathematics Order (ring theory) 010103 numerical & computational mathematics Statistical convergence 01 natural sciences Circle group Combinatorics Mathematics::Group Theory Cardinality Borel subgroup Arithmetic progression 0101 mathematics Mathematics
Zdroj:	Acta Mathematica Hungarica. 162:633-646
ISSN:	1588-2632 0236-5294
DOI:	10.1007/s10474-020-01059-w
Popis:	We introduce a new version of characterized subgroups of the circle group $$\mathbb{T}$$ that we call " $$\alpha$$ -statistically characterized subgroups", in line of the very recent work [11], using the notion of statistical convergence of order $$\alpha$$ [4]. We show that for any arithmetic sequence $$(a_n)$$ and $$\alpha \in (0, 1)$$ , the $$\alpha$$ -statistically characterized subgroups $$t^\alpha_{(a_n)}(\mathbb{T}) $$ is again a Borel subgroup having cardinality $$\mathfrak{c}$$ lying between the characterized and statistically characterized subgroups.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::7b4eeb50daa8638964f069bfdb8c3ccb https://doi.org/10.1007/s10474-020-01059-w Zobrazit plný text záznamu Plný text ve formátu PDF