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Abstrakty
The hierarchy of separation axioms that is familiar from topological spaces generalizes to spaces with an isotone and expansive closure function. Neither additivity nor idempotence of the closure function must be assumed.
Wydawca
Rocznik
Tom
Strony
257--273
Opis fizyczny
Bibliogr. 30 poz., rys., tab.
Twórcy
autor
- Max Planck Institute for Mathematics in the Sciences, Inselstrasse 27, D-04103 Leipzig, Germany
- Institute for Theoretical Chemistry and Molecular Structural Biology, University of Vienna, Währingerstrasse 17, A-1090 Vienna, Austria
autor
- Bioinformatics, Department of Computer Science, University of Leipzig, Kreuzstrasse 7b, D-04103 Leipzig, Inselstrasse 27, D-04103 Leipzig, Germany
- Institute for Theoretical Chemistry and Molecular Structural Biology, University of Vienna, Währingerstrasse 17, A-1090 Vienna, Austria
- The Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
Bibliografia
- [1] H. L. Bentley, E. Lowen-Colebunders, Completely regular spaces, Comment. Math. Univ. Carolinae 32 (1991), 129-154.
- [2] E. Čech, Topological Spaces, Wiley, London, 1966.
- [3] C. H. Cook, H. R. Fischer, Regular convergence spaces, Math. Ann. 174 (1967), 1-7.
- [4] B. A. Davey, H. A. Priestley, Introduction to Lattice and Order, Cambridge Univ. Press, Cambridge UK, 1990.
- [5] M. M. Day, Convergence, closure, and neighborhoods, Duke Math. J. 11 (1944), 181-199.
- [6] U. Eckhardt, L. Latecki, Digital topology, In: Current Topics in Pattern Recognition Research. Council of Scientific Information, Vilayil Gardens, Trivandrum, India, 1994.
- [7] H. R. Fischer, Limesräume, Math. Annalen 137 (1959), 269-303.
- [8] W. Fontana, P. Schuster, Continuity in evolution: On the nature of transitions, Science 280 (1998), 1451-1455.
- [9] W. Fontana, P. Schuster, Shaping space: The possible and the attainable in RNA genotype-phenotype mapping, J. Theor. Biol. 194 (1998), 491-515.
- [10] A. Galton, Continuous motion in discrete space, In: A. G. Cohn, F. Giunchiglia, and B. Selman, editors, Principles of Knowledge Representation and Reasoning: Proceedings of the Seventh International Conference (KR2000), pp. 26-37, San Francisco, CA, 2000, Morgan Kaufmann Publishers.
- [11] G. C. Gastl, P. C. Hammer, Extended Topology. Neighborhoods and Convergents, In: Proceedings of the Colloquium on Convexity 1965, pp. 104-116, Copenhagen, DK, 1967. Københavns Univ. Matematiske Inst.
- [12] P. Gitchoff, G. P. Wagner, Recombination induced hypergraphs: a new approach to mutation-recombination isomorphism, Complexity, 2 (1996), 37-43.
- [13] S. Gniłka, On extended topologies. I: Closure operators, Commentat. Math. Prace Matem. 34 (1994), 81-94.
- [14] S. Gniłka, On extended topologies. II: Compactness, quasi-metrizability, symmetry, Commentat. Math. Prace Matem. 35 (1995), 147-162.
- [15] S. Gniłka, On continuity in extended topologies, Commentat. Math. Prace Matem. 37 (1997), 99-108.
- [16] P. C. Hammer, Extended topology: Set-valued set functions, Nieuw Arch. Wisk. III 10 (1962), 55-77.
- [17] P. C. Hammer, Extended topology: Continuity I, Portug. Math., 25 (1964), 77-93.
- [18] F. Hausdorff, Gestufte Räume, Fund. Math. 25 (1935), 486-502.
- [19] H. H. Keller, Die Limes-Uniformisierbarkeit der Limesräume, Math. Ann. 176 (1968), 334-341.
- [20] D. C. Kent, On convergence groups and convergence uniformities, Fund. Math. 60 (1967), 213-222.
- [21] M. Paoli, E. Ripoli, Convergence subspaces and normality, Ital. J. Pure Appl. Math. 1 (1997), 91-99.
- [22] G. Preuß, Convenient topology, Math. Japonica 47 (1998), 171-183.
- [23] G. Preuss, Higher separation axioms, paracompactness and dimension for semiuniform convergence spaces, Sci. Math. 2 (1999), 321-335.
- [24] A. Rosenfeld, Digital topology, American Mathematical Monthly 86 (1979), 621-630.
- [25] N. Šanin, On separation in topological space, Doki. Akad. Nauk SSSR 38 (1943), 110-113.
- [26] W. P. Soltan, An Introduction in Axiomatic Theory of Convexity, Shtiintsa, Kishinev, 1984 (in Russian).
- [27] B. M. R. Stadler, P. F. Stadler, Generalized topological spaces in evolutionary theory and combinatorial chemistry, J. Chem. Inf. Comput. Sci. 42 (2002), 577-585.
- [28] B. M. R. Stadler, P. F. Stadler, M. Shpak and G. P. Wagner, Recombination spaces, metrics, and pretopologies, Z. Phys. Chem. 216 (2002), 217-234.
- [29] B. M. R. Stadler, P. F. Stadler, G. Wagner and W. Fontana, The topology of the possible: Formal spaces underlying patterns of evolutionary change, J. Theor. Biol. 213 (2001), 241-274.
- [30] D. Thampuran, Normal neighborhood spaces, Rend. Sem. Mat. Univ. Padova 45 (1971), 95-97.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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