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- Title
Continuous Functions in Hashimoto Topologies and Their Algebraic Properties.
- Authors
Bartoszewicz, Artur; Filipczak, Małgorzata; Terepeta, Małgorzata
- Abstract
In the paper we consider the Hashimoto topologies on the interval [ 0 , 1 ] as well as on R , which are connected with the natural topology on R and with some important and well known σ -ideals in P (R) . We study the families of continuous functions f : [ 0 , 1 ] → R with respect to the same Hashimoto topology H (I) (connected with the σ -ideal I ) on the domain and on the range of the considered functions. We show that inside common parts and differences of some such families we can find large (c -generated) free algebras. Some of constructed algebras appear dense in the algebra of the functions which are continuous in the usual sense.
- Publication
Results in Mathematics / Resultate der Mathematik, 2021, Vol 76, Issue 4, p1
- ISSN
1422-6383
- Publication type
Article
- DOI
10.1007/s00025-021-01488-1