Skip to content

Topology


Thomas Mormann


Pages 565 - 568



Topology is a branch of mathematics that investigates formal definitions of notions such as space, continuity, convergence, connectedness, neighbourhood, boundary, closure etc. In philosophical terms, it may be said to provide logical analyses of spatial concepts, where ‘spatial’ is understood in a broad sense. Historically, topology may be considered as a generalisation of metrical geometry. In its modern sense it originated around 1900 and is grounded in the works of Georg Cantor, Felix Hausdorff, Maurice Fréchet, Henri Poincaré and others.




1Department of Logic and Philosophy of Science, University of the Basque Country



1 Davey, B.; Priestley, H., (1990), Introduction to Lattices and Order, Cambridge: Cambridge University Press.

2 Dugundji, J., (1966), Topology, Boston: Allyn and Bacon.

3 Engelking, R., (1989), General Topology, 2nd edition, Berlin: Heldermann.

4 Gierz, G.; Hofmann, K. H.; Keimel, K.; Lawson, J. D.; Mislove, M.; Scott, D. S., (2003), Continuous Lattices and Domains, Cambridge: Cambridge University Press.

5 Grosholz, E., (1980), “Two Episodes in the Unification of Logic and Topology”, The British Journal for the Philosophy of Science 36: 147-157.

6 Hart, K. P.; Nagata, J.; Vaughan, J. E. (eds.), (2004), Encyclopedia of General Topology, Amsterdam: Elsevier.

7 James, I. (ed.), 1999, History of Topology, Amsterdam: North-Holland.

8 Johnstone, P. F., (1982), Stone Spaces, Cambridge: Cambridge University Press.

9 Kunen, K.; Vaughan, J. E. (eds.), (1984), Handbook of Set-Theoretical Topology, Amsterdam: North-Holland.

10 Lewis, D., (1991), Parts of Classes, Oxford: Blackwell.

11 MacLane, S., (1986), Mathematics, Form and Function, Heidelberg and New York: Springer.

12 Mac, Lane, S.; Moerdijk, I., (1992), Sheaves in Geometry and Logic. A First Introduction to Topos Theory, New York: Springer.

13 Nagata, J., (1985), Modern General Topology, 2nd edition, Amsterdam: North-Holland

14 Roeper, P., (1996), “Region-Based Topology”, The Journal of Philosophical Logic 26: 251-309.

15 Smith, B., (1996), “Topology for Philosophers”, The Monist 79 (1).

16 Steen, L.A.; Seebach, J.A., Jr., (1978), Counterexamples in Topology, New York: Springer.

17 Vickers, S., (1989), Topology via Logic, Cambridge: Cambridge University Press.

Share


Export Citation