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

Ewa Korczak-Kubiak; Ryszard J. Pawlak

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 3, page 679-700
  • ISSN: 0011-4642

Abstract

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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, 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.

How to cite

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Korczak-Kubiak, Ewa, and Pawlak, Ryszard J.. "Trajectories, first return limiting notions and rings of $H$-connected and iteratively $H$-connected functions." Czechoslovak Mathematical Journal 63.3 (2013): 679-700. <http://eudml.org/doc/260681>.

@article{Korczak2013,
abstract = {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.},
author = {Korczak-Kubiak, Ewa, Pawlak, Ryszard J.},
journal = {Czechoslovak Mathematical Journal},
keywords = {trajectory; first return continuity; $H$-connected function; ring of functions; D-ring; iteratively $H$-connected function; trajectory; first return continuity; -connected function; ring of functions; D-ring; iteratively -connected function},
language = {eng},
number = {3},
pages = {679-700},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Trajectories, first return limiting notions and rings of $H$-connected and iteratively $H$-connected functions},
url = {http://eudml.org/doc/260681},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Korczak-Kubiak, Ewa
AU - Pawlak, Ryszard J.
TI - Trajectories, first return limiting notions and rings of $H$-connected and iteratively $H$-connected functions
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 3
SP - 679
EP - 700
AB - 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.
LA - eng
KW - trajectory; first return continuity; $H$-connected function; ring of functions; D-ring; iteratively $H$-connected function; trajectory; first return continuity; -connected function; ring of functions; D-ring; iteratively -connected function
UR - http://eudml.org/doc/260681
ER -

References

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