Open AccessOn projections of products of spaces
Author(s) -
A.A. Gryzlov
Publication year - 2021
Publication title -
vestnik udmurtskogo universiteta. matematika, mehanika, kompʹûternye nauki
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.354
H-Index - 8
eISSN - 2076-5959
pISSN - 1994-9197
DOI - 10.35634/vm210304
Subject(s) - uncountable set , countable set , omega , mathematics , product (mathematics) , alpha (finance) , character (mathematics) , combinatorics , product topology , discrete mathematics , pure mathematics , physics , geometry , construct validity , statistics , quantum mechanics , psychometrics
We consider dense sets of products of topological spaces. We prove that in the product $Z^c=\prod\limits_{\alpha\in 2^\omega} Z_{\alpha},$ where $Z_\alpha=Z$ $(\alpha\in 2^\omega),$ there are dense sets such that their countable subsets have projections with additional properties. These properties entail that these dense sets contain no convergent sequences. By these properties we prove that the character of closed sets of the product is uncountable.