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Singular arc-like continua

Seria
Rozprawy Matematyczne tom/nr w serii: 257 wydano: 1986
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Warianty tytułu
Abstrakty
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CONTENTS
Introduction.......................................................................................................5
1. Preliminaries.................................................................................................6
  A. Mappings....................................................................................................6
  B. Arc-like continua.........................................................................................8
  C. Pseudosuspensions...................................................................................8
  D. Set-valued maps........................................................................................9
  E. Cook continua...........................................................................................10
  F. Countable-to-one mappings and admissible compacta.............................10
2. Continua nondivisible by points...................................................................11
  A. V-projections.............................................................................................11
  B. The construction of Σ................................................................................14
3. The function ξ₀............................................................................................16
  A. The construction of $D_β$ and $Σ_β$.....................................................16
  B. The crucial property and its consequences..............................................18
  C. Pseudosuspensions with D and Σ.............................................................20
4. Continua $M_k$ and $N_k$........................................................................21
  A. The construction and properties of $M_k$ and $M̃_k$.............................21
  B. The construction and properties of $N_k$ and $Ñ_k$..............................23
  C. Mappings onto $N_k$...............................................................................24
  D. The slight modifications of $Ñ_k$.............................................................27
  E. The collections N(n)..................................................................................28
5. Zerodimentional sets in $Ñ*_k$...................................................................29
  A. Nice sequences........................................................................................29
  B. The dispersion of zerodimensional sets....................................................30
6. The main construction................................................................................30
References.....................................................................................................34
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 257
Liczba stron
35
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCLVII
Daty
wydano
1986
Twórcy
  • University of Wrocław, Institute of Mathematics, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
  • [1] R. D. Anderson, Atomic decompositions of continua, Duke Math. J. 23 (1956), 507-514.
  • [2] R. D. Anderson and G. Choquet, A plane continuum no two of whose nondegenerate subcontinua are homeomorphic: an application of inverse limits, Proc. Amer. Math. Soc. 10 (1959), 347-353.
  • [3] J. J. Andrews, A chainable continuum no two of whose nondegenerate subcontinua are homeomorphic. Proc. Amer. Math. Soc. 12 (1961), 333-334.
  • [4] D. P. Bellamy, An uncountable collection of chainable continua. Trans. Amer. Math. Soc. 160 (1971), 297-304.
  • [5] R. H. Bing Snake-like continua, Duke Math. J. 18 (1951), 653-663.
  • [6] H. Cook, Continua which admit only the identity mapping onto nondegenerate subcontinua, Fund. Math. 60 (1967), 241-249.
  • [7] A. Emeryk and Z. Horbanowicz, On atomic mappings, Colloq. Math. 27 (1973), 49-55.
  • [8] J. B. Fugate, A characterization of chainable continua, Canadian J. Math. 21 (1969), 383-393.
  • [9] J. de Groot, Continuous mappings of certain family. Fund. Math. 42 (1955), 203-206.
  • [10] B. Knaster, Un continu irréductible à decomposition en tranches. Fund. Math. 25 (1935), 568-577.
  • [11] J. Krasinkiewicz and P. Mine, Nonexistence of universal continua for certain classes of curves, Bull. Acad. Polon. Sci. Ser. Sci. Math, Astronom. Phys. 24 (1976), 733-741.
  • [12] K. Kuratowski, Topology, vol. 11, Polish Scientific Publishers (PWN)-Academic Press, Warsaw-New York, 1968.
  • [13] A. Lelek and D. R. Read, Compositions of confluent mappings and some other classes of functions, Colloq. Math. 29 (1974), 101-112.
  • [14] T. Maćkowiak, Continuous mappings on continua, Dissertationes Math. (Rozprawy Matematyczne) 158 (1979), 1-95.
  • [15] T. Maćkowiak, The condensation of singularities, in arc-like continua, Houston J. Math., to appear.
  • [16] S. Mardevšić and J. Segal, ε-mappings onto polyhedra, Trans. Amer. Math. Soc. 109 (1963), 146-164.
  • [17] J. Mioduszewski, A functional conception of snake-like continua, Fund. Math. 51 (1962), 179-189.
  • [18] L. Mohler and L. Oversteegen, On the structure of tranches in continuously irreducible continua, Colloq. Math, to appear.
  • [19] L. Mohler and L. Oversteegen, A hereditarily indecomposable, hereditarily non-chainable planar tree-like continuum. Fund. Math, to appear.
  • [20] L. Oversteegen and E. Tymchatyn, Subcontinua with degenerate tranches in hereditarily decomposable continua, Trans. Amer. Math. Soc. 278 (1983), 717-724.
  • [21] E. Puzio, Limit mappings and projections of inverse systems. Fund. Math. 80 (1973), 57-73.
  • [22] D. R. Read, Confluent and related mappings, Colloq. Math. 29 (1974), 233-239.
  • [23] J. W. Rogers, Jr., Continuous mappings on continua, Proc. Auburn Topology Conf., March 1969, 94-97.
  • [24] R. E. Smithson, Some general properties of multivalued Junctions, Pacific J. Math. 15 (1965), 681-703.
  • [25] R. E. Smithson, Fixed point theorems for pseudo-monotone mult if unctions, Colloq. Math. 24 (1972), 157-162.
Języki publikacji
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Identyfikator YADDA
bwmeta1.element.zamlynska-33153c56-c061-4fbc-a96f-9bd24b5c1bcd
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ISBN
83-01-07063-3
ISSN
0012-3862
Kolekcja
DML-PL
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