Cancellation of 3-Point Topological Spaces

• Carter, Sheila ^[1] ; Craveiro de Carvalho, F.J. ^[2]
  1. [1] University of Leeds

     University of Leeds

     Reino Unido

     
  2. [2] Universidade de Coimbra

     Universidade de Coimbra

     Coimbra (Sé Nova), Portugal

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 9, Nº. 1, 2008, págs. 15-19
• Idioma: inglés
• DOI: 10.4995/agt.2008.1864
• Enlaces
  • Texto completo
• Resumen

  • The cancellation problem, which goes back to S. Ulam, is formulated as follows: Given topological spaces X, Y, Z, under what circumstances does X × Z ≈Y × Z (≈ meaning homeomorphic to) imply X ≈ Y ? In it is proved that, for T0 topological spaces and denoting by S the Sierpinski space, if X × S≈Y × S then X≈Y. This note concerns all nine (up to homeomorphism) 3-point spaces, which are given in.

• Referencias bibliográficas
  • B. Banaschewski and R. Lowen, A cancellation law for partially ordered sets and T0 spaces, Proc. Amer. Math. Soc. 132 (2004).
  • R. H. Fox, On a problem of S. Ulam concerning cartesian products, Fund. Math. 27 (1947).
  • K. D. Magill Jr, Universal topological spaces, Amer. Math. Monthly 95 (1988).
  • J. R. Munkres, Topology, a first course, Prentice-Hall, Inc., 1975.