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Decomposition of topologies on lattices and hyperspaces

Seria
Rozprawy Matematyczne tom/nr w serii: 381 wydano: 1999
Zawartość
Warianty tytułu
Abstrakty
EN
CONTENTS
Introduction.................................................................................5
1. Decomposable topologies.......................................................6
2. Locally convex topologies......................................................10
3. Semilattices. Strong decomposability.....................................13
4. Convex topologies.................................................................15
5. Topologies on linearly ordered sets.......................................18
6. Topologies on lattices............................................................20
7. The Scott topology.................................................................26
8. Uniqueness of decomposition................................................28
9. Hyperspace topologies..........................................................32
10. The Vietoris topology...........................................................35
11. The Hausdorff metric topology.............................................37
12. The proximal topology..........................................................39
13. The Kuratowski convergence..............................................40
14. Uniqueness of decomposition for hypertopologies..............44
References................................................................................47
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 381
Liczba stron
48
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCLXXXI
Daty
wydano
1999
otrzymano
1998-06-16
poprawiono
1999-02-22
Twórcy
  • Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy
autor
  • Dipartimento di Matematica, Università della Basilicata, via Nazario Sauro 85, 85100 Potenza, Italy
Bibliografia
  • [1] G. A. Beer, C. J. Himmelberg, K. Prikry and F. S. van Vleck, The locally finite topology on $2^X$, Proc. Amer. Math. Soc. 101 (1987), 168-172.
  • [2] G. A. Beer, A. Lechicki, S. Levi and S. A. Naimpally, Distance functionals and suprema of hyperspace topologies, Ann. Mat. Pura Appl. (4) 162 (1992), 367-381.
  • [3] G. A. Beer and R. Lucchetti, Weak topologies for the closed subsets of a metrizable space, Trans. Amer. Math. Soc. 335 (1993), 805-822.
  • [4] C. Costantini, S. Levi and J. Pelant, Infima of hyperspace topologies, Mathematika 83 (1995), 67-86.
  • [5] C. Costantini, S. Levi and J. Zieminska, Metrics that generate the same hyperspace convergence, Set-Valued Anal. 1 (1993), 141-157.
  • [6] C. Costantini and P. Vitolo, On the infimum of the Hausdorff metric topologies, Proc. London Math. Soc. 70 (1995), 441-480.
  • [7] D. E. Dobbs, Posets admitting a unique order-compatible topology, Discrete Math. 41 (1982), 235-240.
  • [8] S. Dolecki, G. H. Greco and A. Lechicki, When do the upper Kuratowski topology (homeomorphically, Scott topology) and the co-compact topology coincide?, Trans. Amer. Math. Soc. 347 (1995), 2869-2884.
  • [9] S. Francaviglia, A. Lechicki and S. Levi, Quasi-uniformization of hyperspaces and convergence of nets of semicontinuous multifunctions, J. Math. Anal. Appl. 112 (1985), 347-370.
  • [10] G. Gierz et al., A Compendium of Continuous Lattices, Springer, New York, 1980.
  • [11] L. Holá and R. Lucchetti, Equivalence among hypertopologies, Set-Valued Anal. 3 (1995), 339-350.
  • [12] S. Levi, R. Lucchetti and J. Pelant, On the infimum of the Hausdorff and Vietoris topologies, Proc. Amer. Math. Soc. 118 (1993), 971-978.
  • [13] E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152-183.
  • [14] J. van Mill and G. M. Reed (eds.), Open Problems in Topology, North-Holland, Amsterdam, 1991.
  • [15] T. Nogura and D. B. Shakhmatov, When does the Fell topology on a hyperspace of closed sets coincide with the meet of the upper Kuratowski and the lower Vietoris topologies?, Topology Appl. 70 (1996), 213-243.
  • [16] H. A. Priestley, Ordered topological spaces and the representation of distributive lattices, Proc. London Math. Soc. 24 (1972), 507-530.
  • [17] P. Vitolo, Strutture d'ordine e topologie sugli iperspazi, PhD thesis, Università degli studi di Milano, Biblioteca Nazionale, Roma-Firenze, 1991.
  • [18] P. Vitolo, Scott topology and Kuratowski convergence on the closed subsets of a topological space, in: Fifth Conf. on Topology (Lecce-Otranto, 1990), Rend. Circolo Mat. Palermo (2) Suppl. 29 (1992), 593-603.
  • [19] H. Weber, Uniform lattices. I: A generalization of topological Riesz spaces and topological boolean rings, Ann. Mat. Pura Appl. (4) 160 (1991), 347-370.
Języki publikacji
EN
Uwagi
1991 Mathematics Subject Classification: Primary 54B20; Secondary 06A12, 54A10.
Identyfikator YADDA
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ISSN
0012-3862
Kolekcja
DML-PL
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