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2013 | 22 | 2 | 139-143

Article title

Special Issue on point-free geometry and topology. An introduction

Title variants

Languages of publication

EN

Abstracts

EN
In the first section we briefly describe the methodological assumptions of point-free geometry and topology. We also outline the history of geometrical theories based on the notion of a region. The second section is devoted to a concise presentation of the content of the LLP special issue on point-free theories of space.

Year

Volume

22

Issue

2

Pages

139-143

Physical description

Dates

published
2013-06-01
online
2013-07-02

Contributors

  • Dipartimento di Matematica Università degli Studi di Salerno via Ponte don Melillo (SA) Italy
  • Dipartimento di Matematica Università degli Studi di Salerno via Ponte don Melillo (SA) Italy

References

  • [1] Casati R., and A. Varzi, “Spatial entities”, in Spatial and Temporal Rea-soning, Oliviero Stock (ed.), Dordrecht, Kluwer, 1997, pp. 73-96 .
  • [2] Clarke, B., “A calculus of individuals based on connection”, Notre DameJournal of Formal Logic, 22 (1981), 3: 204-218.
  • [3] Clarke, B., “Individuals and points”, Notre Dame Journal of Formal Logic 26 (1985), 1: 61-75.
  • [4] De Laguna, T., “Point, line and surface as sets of solids”, The Journal ofPhilosophy, 19 (1922): 449-461.
  • [5] Gerla, G., “Pointless geometries”, in Handbook of Incidence Geometry, F. Buekenhout (ed.), Elsevier Science, 1994, pp. 1015-1031.
  • [6] Gerla, G., and B. Paolillo, “Whitehead’s point-free geometry and diamet- ric posets”, Logic and Logical Philosophy, 19 (2010): 289-308.
  • [7] Grzegorczyk, A., “Axiomatization of geometry without points”, Synthese, 12 (1960): 228-235.
  • [8] Gruszczyński, R., and A. Pietruszczak, “Full development of Tarski’s ge- ometry of solids”, The Bulletin of Symbolic Logic, 14 (2008), 4: 481-540.
  • [9] Lobachevskii, N. I., “New principles of geometry with complete theory of parallels” (in Russian), Polnoe Sobranie Socinenij, 2 (1835).
  • [10] Tarski, A., “Foundations of the geometry of solids”, in Logic, Seman-tics, Metamathematics, J. Corcoran (ed.), Oxford University Press, Ox- ford, 1956, pp. 24-30. Translation of: “Les fondaments de la geometrie des corps”, in Księga Pamiątkowa Pierwszego Polskiego Zjazdu Matema-tycznego, 3 (1929), pp. 29-33.
  • [11] Whitehead, A.N., An Inquiry Concerning the Principles of NaturalKnowledge, Univ. Press. Cambrige, 1919.
  • [12] Whitehead, A.N., The Concept of Nature, Univ. Press. Cambrige, 1920.
  • [13] Whitehead, A.N., Process and Reality, Macmillan, 1929, N.Y.

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.doi-10_2478_llc-2013-0008
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