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Confluent mappings of fans

Seria
Rozprawy Matematyczne tom/nr w serii: 301 wydano: 1990
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Warianty tytułu
Abstrakty
EN

CONTENTS
1. Introduction.......................................................5
2. Preliminaries ....................................................8
3. General properties .........................................11
4. Mappings onto fans........................................14
5. Mappings onto an arc.....................................20
6. A characterization of the top...........................27
7. Open mappings and their lightness................28
8. Inverse limits...................................................39
9. Local connectedness......................................41
10. Planability......................................................43
11. Smoothness..................................................48
12. The property of Kelley...................................57
13. Contractibility................................................67
14. Selectibility....................................................77
15. Final remarks...............................................80
References.........................................................82
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 301
Liczba stron
86
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCI
Daty
wydano
1990
otrzymano
1987-11-19
poprawiono
1989-11-02
Twórcy
  • Institute of Mathematics, University of Wrocław Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
  • Institute of Mathematics, University of Wrocław Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
autor
  • Institute of Mathematics, University of Wrocław Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
  • [1] R. D. Anderson and G. Choquet, A plane continuum no two of whose nondegenerate subcontinua are homeomorphic: on application to inverte limits, Proc. Amer. Math. Soc. 10 (1959), 347-355.
  • [2] D. P. Bellamy, An interesting plane dendroid, Fund. Math. 110 (1980), 191-208.
  • [3] D. P. Bellamy and J. J. Charatonik, The set function T and contractibility of continua, Bull. Acad. Polon. Sci. Sir. Sci. Math. Astronom. Phys. 25 (1977), 47-49.
  • [4] R. B. Bennett, On tome clones of non-contractible dendroids, mimeographed paper, Institute of Mathematics, Polish Academy of Sciences, 1972 (unpublished).
  • [5] K. Borsuk, A countable broom which cannot be imbedded in the plane, Colloq. Math. 10 (1963), 233-236.
  • [6] J. J. Charatonik, On ramification points in the classical sense, Fund. Math. 51 (1962), 229-252.
  • [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.
  • [9] J. J. Charatonik, On fans, Dissertationes Math. (Rozprawy Mat.) 54 (1967), 1-40.
  • [10] J. J. Charatonik, On decompositions of X-dendroids, Fund. Math. 67 (1970), 15-30.
  • [11] J. J. Charatonik, A theorem on monotone mappings of planable A-dendroids, Bull. Acad. Polon. Sci. Sir. Sci. Math. Astronom. Phys. 24 (1976), 171-172.
  • [12] J. J. Charatonik, Problems and remarks on contractibility of curves, in: General Topology and its Relations to Modern Analysis and Algebra IV, Proc. Fourth Prague Topological Symposium, 1976; Part B, Contributed Papers, Society of Czechoslovak Mathematicians and Physicists, Prague 1977, 72-76.
  • [13] J. J. Charatonik, The set function T and homotopies, Colloq. Math. 39 (1978), 271-274.
  • [14] J. J. Charatonik, Open mappings of universal dendrites, Bull. Acad. Polon. Sci. Sir. Sci. Math. 28 (1980), 489-494.
  • [15] J. J. Charatonik, Some recent results and problems in continua theory, Mitt. Math. Gesellsch. DDR 4 (1980), 25-32.
  • [16] J. J. Charatonik, Contractibility and continuous selections, Fund. Math. 108 (1980), 109-118.
  • [17] J. J. Charatonik, Inverse limits of arcs and of simple closed curves with confluent bonding mappings, Period. Math. Hungar. 16 (1985), 219-236.
  • [18] J. J. Charatonik, Some problems on selections and contractibility, Third Topology Conference (Trieste 1986), Rend. Circ. Mat. Palermo (2) Suppl. No. 18 (1988), 27-30.
  • [19] J. J. Charatonik, Conditions related to selectibility (preprint).
  • [20] J. J. Charatonik and W. J. Charatonik, Inverse limits and smoothness of continua, Acta Math. Hungar. 43 (1984), 7-12.
  • [21] J. J. Charatonik and W. J. Charatonik, Monotoneity relative to a point and inverse limits of continua, Glasnik Mat. 20 (40) (1985), 139-151.
  • [22] J. J. Charatonik and W. J. Charatonik, Fans with the property of Kelley, Topology Appl. 29 (1988), 73-78.
  • [23] J. J. Charatonik and W. J. Charatonik, The property of Kelley for fans, Bull. Polish Acad. Sci. Math. 36 (1988), 169-173.
  • [24] J. J. Charatonik and W. J. Charatonik, Images of the Cantor fan, Topology Appl. 33 (1989), 163-172.
  • [25] J. J. Charatonik and C. Eberhart, On smooth dendroids, Fund. Math. 67 (1970), 297-322.
  • [26] J. J. Charatonik and Z. Grabowski, On contractible dendroids, Colloq. Math. 25 (1972), 89-98.
  • [27] J. J. Charatonik and Z. Grabowski, Homotopically fixed arcs and the contractibility of dendroids, Fund. Math. 100 (1978), 229-237.
  • [28] J. J. Charatonik, L. T. Januszkiewics and T. Maćkowiak, An uncountable collection of nonplanable smooth dendroids, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), 147-149.
  • [29] J. J. Charatonik and T.Maćkowiak, Confluent and related mappings on arc-like continua — an application to homogeneity, Topology Appl. 23 (198€j), 29-39.
  • [30] J. J. Charatonik and Z. Rudy, Remarks on non-planable dendroids, Colloq. Math. 37 (1977), 205-216.
  • [31] W. J. Charatonik, Inverse limits of smooth continua, Comment. Math. Univ. Carolinae 23 (1982), 183-191.
  • [32] W. J. Charatonik, Smooth dendroids at inverse limits of dendrites, Fund. Math. 124 (1984), 163-168.
  • [33] W. J. Charatonik, The Lelek fan is unique, Houston J. Math. 15 (1989), 27-34.
  • [34] H. Cook, Continua which admit only the identity mapping onto nondegenerate sub-continua, Fund. Math. 60 (1967), 241-249.
  • [35] S. T. Csuba, R-continua and contractibility of dendroids, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), 299-302.
  • [36] S. T. Csuba, The function T and R-continua, ibid., 303-308.
  • [37] S. T. Csuba, A concept of pointwise smooth dendroids, Uspekhi Mat. Nauk 34 (6) (1979), 215-217 (Russian Math. Surveys 34:6 (1979), 169-171).
  • [38] S. T. Csuba, R'-continua and contractibility, in: Proceedings of the International Conference on Geometric Topology, PWN, Warszawa 1980, 75-79.
  • [39] S. T. Csuba, On pointwise smooth dendroids, Fund. Math. 114 (1981), 197-207.
  • [40] S. T. Csuba, Open functions and pointwise smooth dendroids, in: General Topology and its Relations to Modern Analysis and Algebra V, Proc. Fifth Prague Topological Symposium, 1981, J. Novak (ed.), Heldermann Verlag, Berlin 1982, 118-121.
  • [41] S. T. Csuba, On dendroids with Kelley's property, Proc. Amer. Math. Soc. 102 (1988), 728-730.
  • [42] S. T. Csuba and Z. Karno, A remark concerning hereditary contractibility of some curves (preprint).
  • [43] E. Dyer, Irreducibility of the sum of the elements of a continuous collection of continua, Duke Math. J. 20 (1953), 589-592.
  • [44] E. Dyer, Continuous collections of decomposable continua on a spherical surface, Proc. Amer. Math. Soc. 6 (1955), 351-360.
  • [45] C. A. Eberhart, A note on smooth fans, Colloq. Math. 20 (1969), 89-90.
  • [46] C. A. Eberhart, J. B. Fugate and G. R. Gordh, Jr., Branchpoint covering theorems for confluent and weakly confluent maps, Proc. Amer. Math. Soc. 55 (1976), 409-415.
  • [47] R. Engelking, General topology, PWN, Warszawa 1977.
  • [48] R. Engelking and A. Lelek, Metrizability and weight of inverses under confluent mappings, Colloq. Math. 21 (1970), 239-246.
  • [49] J. B. Fugate, Retracting fans onto finite fans, Fund. Math. 71 (1971), 113-125
  • [50] G. R. Gordh, Jr.,On decompositions of smooth continua, ibid. 75 (1972), 51-60.
  • [51] B. G. Graham, On contractible fans, ibid. 111 (1981), 77-93.
  • [52] J. Grispolakis and E. D. Tymchatyn, On confluent mappings and essential mappings - a survey, Rocky Mountain J. Math. U (1981), 131-153.
  • [53] L. J. Habiniak, There is no plane smooth dendroid containing all plane smooth dendroids, Bull. Acad. Polon. Sci. Sér. Sci. Math. 30 (1982), 465-470.
  • [54] J. L. Kelley, Hyperspaces of a continuum, Trans. Amer. Math. Soc. 52 (1942), 22-36.
  • [55] B. Knaster, Un continu irréductible à décomposition continue en tranches, Fund. Math. 25 (1935), 568-577.
  • [56] B. Knaster, Problem 323, Colloq. Math. 8 (1961), 139.
  • [57] J. Krasinkiewicz and P. Mine, Nonexistence of universal continua for certain classes of curves, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), 733-741.
  • [58] J. Krasinkiewicz and P. Mine, Dendroids and their end points, Fund. Math. 99 (1978), 227-244.
  • [59] J. Krasinkiewicz and P. Mine, Continuous monotone decompositions of planar curves, ibid. 107 (1980), 113-128.
  • [60] W. Kuperberg, Uniformly pathwise connected continua, in: Studies in Topology (Proc. Conf. Univ. North Carolina, Charlotte, N.C. 1974) New York 1975, 315-324.
  • [61] K. Kuratowski, Topology, vol. 1, Academic Press and PWN, 1966.
  • [62] K. Kuratowski, Topology, vol. 2, Academic Press and PWN, 1968.
  • [63] T. J. Lee, Every contractible fan has the bend intersection property, Bull. Polish Acad. Sci. Math. 36 (1988) (to appear).
  • [64] A. Lelek, On plane dendroids and their end points in the classical sense, Fund. Math. 49 (1960/61), 301-319.
  • [65] A. Lelek, On confluent mappings, Colloq. Math. 15 (1966), 223-233.
  • [66] A. Lelek, Some problems concerning curves, ibid. 23 (1971), 93-98.
  • [67] A. Lelek, A classification of mappings pertinent to curve theory, in: Proceedings Univ. Oklahoma Topology Conference 1972, Norman, Oklahoma 1972, 97-103.7-103.
  • [68] A. Lelek, Some union theorems for confluent mappings, Colloq. Math. 31 (1974), 57-65.
  • [69] A. Lelek, Properties of mappings and continua theory, Rocky Mountain J. Math. 6 (1976), 47-59.
  • [70] A. Lelek and D. R. Read, Compositions of confluent mappings and some other classes of functions, Colloq. Math. 29 (1974), 101-112.
  • [71] A. Lelek and E. D. Tymchatyn, Pseudo-confluent mappings and a classification of continua, Canad. J. Math. 27 (1975), 1336-1348.
  • [72] L. Lum, Weakly smooth dendroids, Fund. Math.83 (1974),.111-120.
  • [73] L. Lum, A quasi order characterization of smooth continua, Pacific J. Math. 53 (1974), 495-500.
  • [74] L. Lum, Weakly smooth continua, Trans. Amer. Math. Soc. 214 (1975), 153-167.
  • [75] T. Maćkowiak, Confluent mappings and smoothness of dendroids, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 21 (1973), 719-725.
  • [76] T. Maćkowiak, A note on local homeomorphisms, ibid., 855-858.
  • [77] T. Maćkowiak, Some characterizations of smooth continua, Fund. Math. 79 (1973), 173-186.
  • [78] T. Maćkowiak, Semi confluent mappings and their invariants, ibid., 251-264.
  • [79] T. Maćkowiak, On smooth continua, Fund. Math. 85 (1974), 79-95.
  • [80] T. Maćkowiak, Planable and smooth dendroids, in: General Topology and its Relation to Modern Analysis and Algebra IV, Proc. Fourth Prague Topological Symposium, 1976, Part B, Contributed Papers, Society of Czechoslovak Mathematicians and Physicists, Prague 1977, 260-267.
  • [81] T. Maćkowiak, A certain collection of non-planar fans, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), 543-548.
  • [82] T. Maćkowiak, The hereditary classes of mappings, Fund. Math. 97 (1977), 123-150.
  • [83] T. Maćkowiak, Continuous selections for C(X), Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), 547-551.
  • [84] T. Maćkowiak, Continuous mappings on continua, Dissertationes Math. (Rozprawy Mat.) 158 (1979), 1-91.
  • [85] T. Maćkowiak, Contractible and nonselectible dendroids, Bull. Polish Acad. Sci. Math. 33
  • (1985), 321-324.
  • [86] R. Mańka, Ramification order of a curve and confluent mappings of fans, M. Sc. Thesis, Wrocław University 1970 (in Polish; unpublished).
  • [87] M. M. Marsh, A fixed point theorem for inverse limits of fans, Proc. Amer. Math. Soc. 91 (1984), 139-142.
  • [88] M. M. Marsh, A fixed point theorem for inverse limits of simple n-ods, Topology Appl. 24
  • (1986), 213-216.
  • [89] M. M. Marsh, Mappings of trees and the fixed point property, Trans. Amer. Math. Soc. (to appear).
  • [90] T. B. McLean, Confluent images of tree-like curves are tree-like, Duke Math. J. 39 (1972), 465-473.
  • [91] L. Mohler, A characterization of smoothness in dendroids, Fund. Math. 67 (1970), 369-376.
  • [92] S. B. Nadler, Jr., Inverse limits and multicoherence, Bull. Amer. Math. Soc. 76 (1970), 411-414.
  • [93] S. B. Nadler, Jr., Multicoherence techniques applied to inverse limits, Trans. Amer. Math. Soc. 157 (1971), 227-234.
  • [94] S. B. Nadler, Jr., Problem 906 in the New Scottish Book, dated December 13, 1974 (unpublished).
  • [95] S. B. Nadler, Jr., Concerning completeness of the space of confluent mappings, Houston J. Math. 2 (1976), 561-580.
  • [96] S. B. Nadler, Jr., Confluent images of the sinusoidal curve, Houston J. Math. 3 (1977), 515-519.
  • [97] S. B. Nadler, Jr., Hyperspaces of sets, Pure and Applied Math. 49, M. Dekker, New York and Basel 1978.
  • [98] S. B. Nadler, Jr., The metric confluent images of half lines and lines, Fund. Math. 102 (1979), 183-194.
  • [99] S. B. Nadler, Jr. and L. E. Ward, Jr., Concerning continuous selections, Proc. Amer. Math. Soc. 25 (1970), 369-374.
  • [100] J. Nikiel, A characterization of dendroids with uncountably many end points in the classical sense, Houston J. Math. 9 (1983), 421-432.
  • [101] J. Nikiel, On dendroids and their ramification points in the classical sense, Fund. Math. 123 (1984), 39-46.
  • [102] J. Nikiel, On dendroids and their end points and ramification points in the classical sense, ibid. 124 (1984), 99-108.
  • [103] J. Nikiel, On Gehman dendroids, Glasnik Mat. 20 (40) (1985), 203-214.
  • [104] L. G. Oversteegen, Non-contractibility of continua, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 26 (1978), 837-840.
  • [105] L. G. Oversteegen, Internal characterizations of contractibility of fans, ibid. 27 (1979), 391-395.
  • [106] L. G. Oversteegen, Fans and embeddings in the plane, Pacific J. Math. 83 (1979), 495-503.
  • [107] L. G. Oversteegen, Every contractible fan it locally connected at its vertex, Trans. Amer. Math. Soc. 260 (1980), 379-402.
  • [108] L. G. Oversteegen, Open retractions and locally confluent mappings of certain continua, Houston J. Math. 6 (1980), 113-125.
  • [109] D. R. Read, Confluent and related mappings, Colloq. Math. 29 (1974), 233-239.
  • [110] D. R. Read, Irreducibly confluent mappings, ibid. 34 (1975), 49-55.
  • Confluent mappings of fans
  • [111] R. L. Russo, Universal continua, Fund. Math. 105 (1979), 41-60.
  • [112] A. D. Wallace, Quasi-monotone transformations, Duke Math. J. 7 (1940), 136-145.
  • [113] L. E. Ward, Jr., Mobs, trees and fired points, Proc. Amer. Math. Soc. 8 (1957), 798-804.
  • [114] L. E. Ward, Jr., Rigid selections and smooth dendroids, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 19 (1971), 1041-1043.
  • [115] R. W. Wardle, On a property of Kelley, Houston J. Math. 3 (1977), 291-299.
  • [116] G. T. Whyburn, Analytic topology, Amer. Math. Soc. Colloq. Publ. 28, Providence 1942.
  • [117] D. Zaremba, On cohesive mappings, in: General Topology and its Relation to Modern Analysis and Algebra IV, Proc. Fourth Prague Topological Symposium 1976, Part B, Contributed Papers, Society of Czechoslovak Mathematicians and Physicists, Prague 1977, 527-530.
  • [118] D. Zaremba, Concerning confluent mappings and quasi-interior mappings, Bull. Acad. Polon. Sci. Sir. Sci. Math. 29 (1981), 279-283.
Języki publikacji
EN
Uwagi
1985 Mathematics Subject Classification 54F50, 54F20, 54C10
Identyfikator YADDA
bwmeta1.element.zamlynska-4cdb7749-8dd8-408a-a2e8-bfc149f89a8b
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ISBN
83-85-116-00-1
ISSN
0012-3862
Kolekcja
DML-PL
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