Journey into Apartness Space
We present some of the fundamental notions and results in the axiomatic theory of apartness spaces, a constructive approach to topology. The paper begins with apartness between sets, and between points and sets, and ends with very recent work on the theory of apartness on frames.
KeywordsTopological Space Uniform Convergence Intuitionistic Logic Uniform Structure Uniform Space
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- 1.P. Aczel and M. Rathjen, Notes on Constructive Set Theory, Report No. 40, Institut Mittag-Leffler, Royal Swedish Academy of Sciences, 2001.Google Scholar
- 7.D.S. Bridges and L.S. Vîţă, Apartness Spaces, research monograph, in preparation.Google Scholar
- 10.P. Cameron, J.G. Hocking, and S.A. Naimpally, ‘Nearness—a better approach to continuity and limits’, Amer. Math. Monthly, Sept. 1974, 739–745.Google Scholar
- 11.G. Curi, ‘Notes on ‘Apartness Spaces as Formal Spaces”, preprint, Università di Padova, Padova.Google Scholar
- 15.R. Milošević, D.A. Romano, and M. Vinčić, ‘A basic separation on a set with apartness’, Publikacije Elektr. Fakult. Univ. u Beogradu 8, 37-43, 1997.Google Scholar
- 16.L.J. Nachman, Weak and Strong Constructions in Proximity Spaces, Ph.D. dissertation, The Ohio State University, 1968.Google Scholar
- 17.S.A. Naimpally and B.D. Warrack, Proximity Spaces, Cambridge Tracts in Math. and Math. Phys. 59, Cambridge at the University Press, 1970.Google Scholar
- 19.G. Sambin, ‘Intuitionistic formal spaces—a first communication’, in: Mathematical Logic and its Applications (D. Skordev, ed.), 187–204, Plenum Press, New York, 1987.Google Scholar
- 24.F. Waaldijk, Modern Intuitionistic Topology, Ph.D. thesis, University of Nijmegen, Netherlands, 1996.Google Scholar