Given any dimension function h, we construct a perfect set E of zero h-Hausdorff measure, that contains any finite polynomial pattern.This is achieved as a special case of a more general construction in which we have a family of functions that satisfy certain conditions and we construct a perfect set E in, of h-Hausdorff measure zero, such that for any finite set {f1,.,fn} †, E satisfies that.We also obtain an analogous result for the images of functions. Additionally we prove some related results for countable (not necessarily finite) intersections, obtaining, instead of a perfect set, an set without isolated points. © 2018 Cambridge Philosophical Society.
Documento: | Artículo |
Título: | Small sets containing any pattern |
Autor: | Molter, U.; Yavicoli, A. |
Filiación: | Departamento de Matemática and IMAS/UBA-CONICET, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Argentina |
Año: | 2018 |
DOI: | http://dx.doi.org/10.1017/S0305004118000567 |
Título revista: | Mathematical Proceedings of the Cambridge Philosophical Society |
Título revista abreviado: | Math. Proc. Camb. Philos. Soc. |
ISSN: | 03050041 |
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03050041_v_n_p_Molter |