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Non-Hausdorff Ascoli theory

Seria
Rozprawy Matematyczne tom/nr w serii: 119 wydano: 1974
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Abstrakty
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CONTENTS

Introduction......................................................................................................................................... 5
Chapter I. THEORY IN CLASSICAL POEM FOB FUNCTIONS
  1. Equicontinuity in quasi-uniform context................................................................... 6
  2. Quasi-uniform convergence on compacta............................................................. 8
  3. k-spaces and $k_3$,-spaces................................................................................... 9
  4. A separating equivalence relation............................................................................ 11
  5. Ascoli theorem............................................................................................................. 11

Chapter II. TOPOLOGICAL THEORY FOR MULTIFUNCTIONS
  6. Preliminary lemmas for multifunctions................................................................... 14
  7. Tychonoff theorem for multifunctions....................................................................... 16
  8. Exponential law for multifunctions............................................................................ 18
  9. Product of two k-spaces............................................................................................. 20
  10. Non-Hausdorff theorem of the Gale type.............................................................. 21
  11. Non-Hausdorff theorem of the Kelley—Morse type............................................ 24

Chapter III. UNIFORM THEORY FOR MULTIFUNCTIONS
  12. Ascoli theorems......................................................................................................... 27
  13. Reduction to function context.................................................................................. 32
References.................................................................................................................................................. 36
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 119
Liczba stron
37
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CXIX
Daty
wydano
1974
Twórcy
  • Université de Montréal, Montréal
Bibliografia
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  • [3] С. Вorge, Espaces topologiques, fonctions multivoques, Paris 1959.
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  • [6] A. Császár, Fondement de la topologie générale, Paris 1960.
  • [7] J. M. Gr. Fell, A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff space, Proc. Amer. Math. Soc. 13 (1962), pp. 472-476.
  • [8] J. Flachsmeyer, Verschiedene Topologisierungen im Raum der abgeschlossenen Mengen, Math. Nachr. 26 (1964), pp. 321-337.
  • [9] G. Fox and P. Morales, A non-Hausdorff Ascoli theorem for $k_3$ spaces, Proc. Amer. Math. Soc. 39 (1973), pp. 633-636.
  • [10] G. Fox and P. Morales, A general Tychonoff theorem for multifunctions, Canad. Math. Bull. (to appear).
  • [11] R. H. Fox, On topologies for function spaces, Bull. Amer. Math. Soc. 51 (1945), pp. 429-432.
  • [12] O. Frink, Topology in lattices, Trans. Amer. Math, Soc. 51 (1942), pp. 569-582.
  • [13] D. Gale, Compact sets of functions and function rings, Proc. Amer. Math. Soc. 1 (1950), pp. 303-308.
  • [14] J. Kelley, General topology, New York 1965.
  • [15] Y. F. Lin, Tychonoff's theorem, for the space of multifunctions, Amer. Math. Monthly 74 (1967), pp. 399-400.
  • [16] Y. F. Lin and D. A. Rose, Ascoli's theorem for spaces of multifunctions, Pacific J. Math. 34 (1970), pp. 741-747.
  • [17] V. J. Mancuso, An Ascoli theorem for multi-valued functions, J. Austral. Math. Soc. 12 (1971), pp. 466-472.
  • [18] E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), pp. 152-182.
  • [19] E. Michael, Local compactness and Cartesian products of quotient maps and k-spaces, Ann. Inst. Fourier (Grenoble) 18 (1968), pp. 281-286.
  • [20] P. Morales, Pointwise compact spaces, Canad. Math. Bull. (to appear).
  • [21] P. Morales, Théorèmes non-Hausdorff d'Ascoli pour fonctions et fonctions multivoques, Thèse de Doctorat, Université de Montréal 1973.
  • [22] M. G. Murdeshwar and S. A. Naimpally, Quasi-uniform topological spaces, Noordhoff 1966.
  • [23] S. В. Myers, Equicontinuous sets of mappings, Ann. of Math. 47 (1946), pp. 496-502.
  • [24] N. Noble, Ascoli theorems and the exponential map, Trans. Amer. Soc. 143 (1969), pp. 393-411.
  • [25] N. Noble, The continuity of functions on cartesian products, ibid. 149 (1970), pp. 187-198.
  • [26] W. J. Pervin, Quasi-uniformization of topological spaces, Math. Ann. 147 (1962), pp. 316-317.
  • [27] V. I. Ponomarev, Properties of topological spaces preserved under multi-valued continuous mappings, Mat. Sb. (N.S.) 51 (93) (1960), pp. 515-536 = Math. Soc. Transl. (2) 38 (1968), pp. 119-140.
  • [28] H. Poppe, Stetige Konvergenz und der Satz von Ascoli und Arzelà, Math. Nachr. 30 (1965), pp. 87-122.
  • [29] H. Poppe, Stetige Konvergent und der Satz von Ascoli und Arzelà, III, IV, V, VI, Proc. Japan Acad. 44 (1968), pp. 234-242 and 318-324.
  • [30] R. E. Smithson, Some general properties of multi-valued functions, Pacific J. Math. 15 (1965), pp. 681-703.
  • [31] R. E. Smithson, Topologies on sets of relations, J. Nat. Sci. and Math. (Lahore) 11 (1971), pp. 43-50.
  • [32] R. E. Smithson, Uniform convergence for multifunctions, Pacific J. Math. 30 (1971), pp. 253-259.
  • [33] R. E. Smithson, Multifunction, Nieuw Arch. Wisk. 20 (1972), pp. 31-53.
  • [34] W. L. Strother, Continuous multi-valued functions, Bol. Soc.Mat. Sao Paulo 10 (1955), pp. 87-120.
  • [35] W. L. Strother, Multi-homotopy, Duke Math. J. 22 (1955), pp. 281-285.
  • [36] W. L. Strother, Fixed points, fixed sets and M-retraots, ibid. 22 (1955), pp. 551-556.
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