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

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Hofmann K. H., Stralka A.

Instytut Matematyczny Polskiej Akademii Nauk

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

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1 Hofmann K. H.

1 Stralka A.

1 1976

Wyniki wyszukiwania

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