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Limits and colimits in certain categories of spaces of continuous functions

Seria
Rozprawy Matematyczne tom/nr w serii: 79 wydano: 1970
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Warianty tytułu
Abstrakty
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CONTENTS
Introduction................................................................................................................................................................................5
§ 1. Notation and preliminaries.............................................................................................................................................6
§ 2. Epimorphisms and monomorphisms.........................................................................................................................7
§ 3. Completeness and cocompleteness of the categories ℋ, $\bar{ℋ}$, $ℋ_S$ and ℋ 0$\bar{ℋ}_S$.........9
§ 4. Limits and colimits in $\bar{ℋ}$ in terms of limits and colimits in Arch and Compconv..................................14
§ 5. Limits and colimits in Compconv in terms of limits and colimits in $\bar{ℋ}$....................................................23
§ 6. Retracts and free objects................................................................................................................................................32
References................................................................................................................................................................................35
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 79
Liczba stron
36
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom LXXIX
Daty
wydano
1970
Twórcy
  • Temple University Philadelphia, PA.
Bibliografia
  • [1] E. M. Alfsen, Boundary values for homomorphisms of compact convex sets, Math. Scand. 19 (1966), pp. 113-121.
  • [2] E. M. Alfsen, Facial structure of compact convex sets, Proc. London Math. Soc. (3) 18 (1968), pp. 385-404.
  • [3] E. M. Alfsen, On the Dirichlet problem of the Choquet boundary (to appear).
  • [4] H. Bauer, Silovscher Rand und Dirichletsches Problem, Ann. Inst. Fourier, Grenoble 11 (1961), pp. 89-136.
  • [5] H. Bauer, Aspects of linearity in the theory of function algebras, Function Algebras, Proceedings of an International Symposium on Function Algebras held at Tulane University, 1965. pp. 122-137.
  • [6] E. Bishop and K. de Leeuw, The representation of linear functionals by measures on sets of extreme points, Ann. Inst. Fourier, Grenoble 9 (1969), pp. 306-331.
  • [7] G. Choquet and P. A. Meyer, Existence et unicité des représentations intégrales dans les convexes compact quelconques, Ann. Inst. Fourier, Grenoble 13 (1963), pp. 139-154.
  • [8] E. B. Davies and G. F. Vincent-Smith, Tensor products, infinite products and projective limits of Choquet simplexes, Math. Scand. 22 (1968), pp. 145-164.
  • [9] J. Dugundji, Topology, Boston, 1966.
  • [10] D. A. Edwards, On the representation of certain functionals by measures on the Choquet boundary, Ann. Inst. Fourier, Grenoble 13 (1963), pp. 111-121.
  • [11] D. A. Edwards, Introduction to Functional Analysis, Lecture notes at Lehigh University by A. J. Ellis, 1964.
  • [12] P. Freyd, Abelian Categories, New York, 1964.
  • [13] M. W. Grossman, A Choquet boundary for the product of two compact spaces, Proc. Amer. Math. Soc. 16 (1965), pp. 967-971.
  • [14] M. W. Grossman, Relative Choquet and Šilov boundaries, J. Reine Angew. Math. 225 (1967), pp. 1-29.
  • [15] M. W. Grossman, An extremal property for certain spaces of lower semi-continuous functions, Math. Z. 106 (1968), pp. 139-148.
  • [16] A. Hulanicki and R. R. Phelps, Some applications of tensor products of partially ordered linear spaces, J. Functional Analysis 2 (1968), 177-201.
  • [17] F. Jellett, Homomorphisms and inverse limits of Choquet simplexes, Math. Z. 103 (1968), pp. 219-226.
  • [18] A. J. Lazar, Affine products of simplexes, Math. Scand. 22 (1968), pp. 165-175.
  • [19] G. Lion, Familles d'opérateurs et frontières en théorie du potentiel, Ann. Inst. Fourier, Grenoble 16 (1966), pp. 389-453.
  • [20] B. Mitchell, Theory of Categories, New York, 1965.
  • [21] R. R. Phelps, Lectures on Choquet's Theorem, Princeton, 1966.
  • [22] Z. Semadeni, Free and direct objects, Bull. Amer. Math. Soc. 69 (1963), pp. 63-66.
  • [23] Z. Semadeni, Spaces of continuous functions on compact sets, Adv. in Math. 1 (1965), pp. 320-382.
  • [24] Z. Semadeni, Free compact convex sets, Bull. Acad. Sci. Polon. 13 (1965), pp. 141-146.
  • [25] Z. Semadeni, Categorical methods in convexity, Proc. Coll. Convexity, Copenhagen, 1965 (1967), pp. 281-307.
  • [26] Z. Semadeni, Projectivity, injectivity and duality, Rozprawy Matematyczne 35 (1963), pp. 1-47.
  • [27] Z. Semadeni, Free objects in the theory of categories, Colloq. Math. 14 (1966), pp. 107-110.
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