Mapping hierarchy for dendrites

Charatonik, J. J.; Charatonik, W. J.; Prajs, J. R.

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Tytuł książki

Mapping hierarchy for dendrites

Autorzy

J. J. Charatonik W. J. Charatonik J. R. Prajs

Seria

Rozprawy Matematyczne tom/nr w serii: 333 wydano: 1994

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Abstrakty

Abstract
Let a family S of spaces and a class F of mappings between members of S be given. For two spaces X and Y in S we define $Y ≤_F X$ if there exists a surjection f ∈ F of X onto Y. We investigate the quasi-order $≤_F$ in the family of dendrites, where F is one of the following classes of mappings: retractions, monotone, open, confluent or weakly confluent mappings. In particular, we investigate minimal and maximal elements, chains and antichains in the quasi-order $≤_{F}$, and characterize spaces which can be mapped onto some universal dendrites under mappings belonging to the considered classes.

CONTENTS
1. Introduction..................................................................5
2. Preliminaries................................................................6
3. Hierarchy of spaces.....................................................7
4. Dendrites.....................................................................9
5. Monotone and confluent mappings............................13
6. Open mappings ........................................................22
7. Problems ...................................................................51
References....................................................................51

Słowa kluczowe

continuum confluent dendrite monotone mapping open mapping light mapping

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Seria

Rozprawy Matematyczne tom/nr w serii: 333

Liczba stron

Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCCXXXIII

Daty

wydano

1994

otrzymano

1993-02-08

poprawiono

1993-07-06

Twórcy

autor

J. J. Charatonik

Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

W. J. Charatonik

Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

J. R. Prajs

Institute of Mathematics, Pedagogical University, ul. Oleska 48, 45-951 Opole, Poland

Bibliografia

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[7] J. J. Charatonik, Two invariants under continuity and the incomparability of fans, ibid. 53 (1964), 187-204.
[8] J. J. Charatonik, Confluent mappings and unicoherence of continua, ibid. 56 (1964), 213-220.
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[11] J. J. Charatonik, Monotone mappings of universal dendrites, Topology Appl. 38 (1991), 163-187.
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[22] K. Kuratowski et G. T. Whyburn, Sur les éléments cycliques et leurs applications, Fund. Math. 16 (1930), 305-331.
[23] L. Lum, A characterization of local connectivity in dendroids, in: Studies in Topology, Academic Press, New York, 1975, 331-338.
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[31] J. Nikiel, A characterization of dendroids with uncountably many end points in the classical sense, Houston J. Math. 9 (1983), 421-432.
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[37] G. T. Whyburn, Analytic Topology, Amer. Math. Soc., 1942.

Języki publikacji

Uwagi

1991 Mathematics Subject Classification: 54C10, 54F50.

Identyfikator YADDA

bwmeta1.element.zamlynska-eea5baf4-e92e-463d-a429-a0f6796efcba

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ISSN

0012-3862

Kolekcja

DML-PL

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