Article

 Title: Trajectories, first return limiting notions and rings of $H$-connected and iteratively $H$-connected functions (English) Author: Korczak-Kubiak, Ewa Author: Pawlak, Ryszard J. Language: English Journal: Czechoslovak Mathematical Journal ISSN: 0011-4642 (print) ISSN: 1572-9141 (online) Volume: 63 Issue: 3 Year: 2013 Pages: 679-700 Summary lang: English . Category: math . Summary: In the paper the existing results concerning a special kind of trajectories and the theory of first return continuous functions connected with them are used to examine some algebraic properties of classes of functions. To that end we define a new class of functions (denoted $Conn^*$) contained between the families (widely described in literature) of Darboux Baire 1 functions (${\rm DB}_1$) and connectivity functions ($Conn$). The solutions to our problems are based, among other, on the suitable construction of the ring, which turned out to be in some senses an “optimal construction“. These considerations concern mainly real functions defined on $[0,1]$ but in the last chapter we also extend them to the case of real valued iteratively $H$-connected functions defined on topological spaces. (English) Keyword: trajectory Keyword: first return continuity Keyword: $H$-connected function Keyword: ring of functions Keyword: D-ring Keyword: iteratively $H$-connected function MSC: 26A15 MSC: 26A21 MSC: 54C30 MSC: 54C40 MSC: 54H20 idZBL: Zbl 06282105 idMR: MR3125649 DOI: 10.1007/s10587-013-0047-8 . Date available: 2013-10-07T12:03:57Z Last updated: 2020-07-03 Stable URL: http://hdl.handle.net/10338.dmlcz/143484 . Reference: [1] Bąkowska, A., Loranty, A., Pawlak, R. J.: On the topological entropy of continuous and almost continuous functions.Topology Appl. 158 (2011), 2022-2033. Zbl 1227.54022, MR 2825356, 10.1016/j.topol.2011.06.049 Reference: [2] Biś, A., Nakayama, H., Walczak, P.: Modelling minimal foliated spaces with positive entropy.Hokkaido Math. J. 36 (2007), 283-310. 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