Proximal Connectedness

• Autorzy: Bridges D.S. , Vîta L.S.
• Języki publikacji: EN

Abstrakty

EN

A notion of connectedness is introduced into the theory of apartness spaces, and various fundamental properties of connected sets are established.

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2008
• Tom: Vol. 83, nr 1-2
• Strony: 25--34
• Opis fizyczny: bibliogr. 17 poz.

Twórcy

autor

Bridges D.S.

autor

Vîta L.S.

• Department of mathematics and Statistics University of Canterbury Private Bag 4800 Chrstchurch, New Zeeland,

Bibliografia

• [1] E.A. Bishop, Foundations of Constructive Analysis, McGraw-Hill, New York, 1967.
• [2] E.A. Bishop and D.S. Bridges, Constructive Analysis, Grundlehren der Math. Wiss. 279, Springer-Verlag, Heidelberg, 1985.
• [3] D.S. Bridges, 'A constructive look at the real number line', in: Real Numbers, Generalizations of the Reals, and Theories of Continuum (P. Ehrlich, ed.), Synthese Library 242,29-92, 1994.
• [4] D.S. Bridges and F. Richman, Varieties of Constructive Mathematics, London Math. Soc. Lecture Notes 97, Cambridge Univ. Press, 1987.
• [5] D.S. Bridges, L.S. Vifa, 'Apartness spaces as a framework for constructive topology', Ann. Pure Appl. Logic. 119(1-3), 61-83,2003.
• [6] D.S. Bridges, L.S. Vffa, Techniques of Constructive Analysis, Universitext, Springer-New-York, 2006.
• [7] D.S. Bridges, L.S. Vi{a, Apartness Spaces, monograph, in preparation.
• [8] D.S. Bridges, H. Ishihara, P.M. Schuster, L.S. Vffa, 'Products in the category of apartness spaces', Cahiers de Topologie et Geometrie Differentielle 46, 139-153,2005.
• [9] M. Hazewinkel (ed.), Soviet Encyclopaedia of Mathematics, Vol. 7, Kluwer Academic Publishers, Dordrecht, 1991.
• [10] H. Ishihara, 'Continuity properties in constructive mathematics', J. Symbolic Logic 57(2), 557-565, 1992.
• [11] M. Mandelkern, 'Connectivity of an interval', Proc. Amer. Math. Soc. 54, 170-172, 1976.
• [12] S. Naimpally and B. Warrack, Proximity Spaces, Cambridge Tracts in Math, and Math. Phys. 59, Cambridge University Press, 1970.
• [13] P.M. Schuster, L.S. Vfja, D.S. Bridges, 'Apartness as a relation between subsets', in: Combinatorics, Com-putability and Logic (Proceedings of DMTCS'Ol, Constanta, Romania, 2-6 July 2001; C.S. Calude, M.J. Dinneen, S. Sburlan (eds.)), 203-214, DMTCS Series 17, Springer-Verlag, London, 2001.
• [14] A.S. Troelstra and D. van Dalen, Constructivism in Mathematics (2 vols), Studies in Logic and the Foundations of Mathematics 121, North-Holland, Amsterdam, 1988.
• [15] L.S. Vfja, 'Separation properties of apartness spaces', preprint, University of Canterbury, 2004.
• [16] L.S. Vita, 'On Complements of Sets and the Efremovic Condition', J. Univ. Comp. Science 11(12), 2159-2164,2005.
• [17] L.S. Vfja, D.S. Bridges, 'A constructive theory of point-set nearness', Topology in Computer Science: Con-structivity; Asymmetry and Partiality; Digitization (Proc. Dagstuhl Seminar 00231,4-9 June 2000; R. Kop-perman, M. Smyth, D. Spreen, eds.), Theoretical Computer Science 305 (1-3), 473-489,2003