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The algebraic theory of compact Lawson semilattices Applications of Galois connections to compact semilattices

Seria
Rozprawy Matematyczne tom/nr w serii: 137 wydano: 1976
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Abstrakty
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CONTENTS

Introduction....................................................................................................................................... 5
 List of categories........................................................................................................................ 8
1. GALOIS CONNECTIONS................................................................................................................... 10
 a. The basic theory of Galois connections............................................................................. 10
 b. Applications of Galois connections to compact semilattices........................................ 13
 c. Supplementary results on Lawson semilattices.............................................................. 16
2. COMPACT ZERO-DIMENSIONAL SEMILATTICES WITH COMPLETE DUAL............................. 19
 a. Dual completeness............................................................................................................... 19
 b. The compact closure operator............................................................................................. 21
 c. Algebraic and order theoretic characterization of Lawson semilattices....................... 24
 d. The functoriality of j, c, m......................................................................................................... 28
3. THE (RIGHT) REFLECTOR P : CL → D
 a. The ideal lattice......................................................................................................................... 33
 b. The morphism $s_L : L → PL$.............................................................................................. 35
 c. The functor P : CL → D............................................................................................................. 36
 d. PL as a projective object......................................................................................................... 37
4. ON THE FINE STRUCTURE OF PL................................................................................................... 42
 a. The construction of A(L).......................................................................................................... 42
 b. On the geometric structure of PL........................................................................................... 47
5. EXAMPLES, APPLICATIONS................................................................................................................ 50

Bibliography........................................................................................................................................ 54
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 137
Liczba stron
54
Liczba rozdzia³ów
Opis fizyczny
Dissertationes mathematicae, Tom CXXXVII
Daty
wydano
1976
Bibliografia
  • [1] Aumann, G., Bemerkung über Galois-Verbindungen, Bayer. Akad. Wisa. Math.-Nat. Kl. S.-B. (1955), pp. 281-284.
  • [2] Blyth, T. S., and M. F. Janowitz, Residuation Theory, Pergamon, Oxford, 1972.
  • [3] Bruns, G., A lemma on directed sets and chains, Arch, der Math. 18 (1967), pp. 561-563.
  • [4] Derderian, J. C., Residuated mappings, Pacific J. Math. 20 (1967), pp. 35-43.
  • [5] Everett, C. J., Closure operators and Galois theory in lattices, Trans. Amer. Math. Soc. 55 (1944), 514-525.
  • [6] Geissinger, L., and W. Graves, The category of complete algebraic lattices, J. Combinatorial Theory (A) 13 (1972), pp. 332-338.
  • [7] Hofmann, K. H. and M. Mislove, Lawson semilattices do have a Pontryagin duality, Proc. Univ. Houston Lattice Theory Conf. 1973, pp. 200-205.
  • [8] Hofmann, K. H., M. Mislove and A. Stralka, The Pontryagin Duality of Compact 0-Dimensional Semilattices and its Applications, Lecture Notes in Math. 396, Springer-Verlag, Heidelberg, 1974.
  • [9] Hofmann, K. H., Dimension raising maps in topological algebra, Math. Zeit. 135 (1973), pp. 1-36.
  • [10] Hofmann, K. H. and A. R. Stralka, Push-outs and strict projective limits of semilattices, Semigroup Forum 5 (1973), pp. 243-261.
  • [11] Hofmann, K. H., Mapping cylinders and compact monoids, Math. Ann. 205 (1973), pp. 219-239.
  • [12] Lawson, J. D., Topological semilattices with small semilattices, J. London Math. Soc. II Ser. I (1969), pp. 719-724.
  • [13] Lawson, J. D., Lattices with no interval homomorphisms, Pacific J. Math. 32 (1970), pp. pp. 459-465.
  • [14] Lawson, J. D., Intrinsic topologies in topological lattices and semilattices, Pacific J. Math. 44 (1973), pp. 593-602.
  • [15] MacLane, S., Categories for the Working Mathematician, Springer-Verlag, New York, 1971.
  • [16] Ore, O., Galois connections, Trans. Amer. Math. Soc. 55 (1944), pp. 493-513.
  • [17] Pickert, G., Bemerkungen über Galois-Verbindungen, Arch. Math. 3 (1952), pp. 285-289.
  • [18] Raney, G. N., Tight Galois connections and complete diftributivily, Trans. Amer. Math. Soc. 97 (1960), pp. 418-426.
  • [19] Schmidt, J., Each join-completion of a partially ordered set is the solution of a universal problem, J. Austral. Math. Soc. 16 (1973).
  • [20] Hofmann, K. H., and M. Mislove, Epimorphisms of Lawson semilattices, Arch, der Math. 26(1975), pp. 337-345.
Języki publikacji
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Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-0a64c2e4-4598-4b8a-9017-1624fd87ce6b
Identyfikatory
Kolekcja
DML-PL
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