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Trajectories, first return limiting notions and rings of $H$ -connected and iteratively $H$ -connected functions

Ewa Korczak-Kubiak; Ryszard J. Pawlak — 2013

Czechoslovak Mathematical Journal

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 $C o n n^{*}$ ) contained between the families (widely described in literature) of Darboux Baire 1 functions ( ${DB}_{1}$ ) and connectivity functions ( $C o n n$ ). The solutions to our problems are based, among other, on the suitable construction of the ring,...

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Trajectories, first return limiting notions and rings of H -connected and iteratively H -connected functions

Trajectories, first return limiting notions and rings of $H$ -connected and iteratively $H$ -connected functions