Cancellation of 3-Point Topological Spaces


  • Sheila Carter University of Leeds
  • F.J. Craveiro de Carvalho Universidade de Coimbra



Homeomorphism, Cancellation problem, 3-point spaces


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.


Download data is not yet available.

Author Biographies

Sheila Carter, University of Leeds

School of Mathematics

F.J. Craveiro de Carvalho, Universidade de Coimbra

Departamento de Matemática


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.


How to Cite

S. Carter and F. Craveiro de Carvalho, “Cancellation of 3-Point Topological Spaces”, Appl. Gen. Topol., vol. 9, no. 1, pp. 15–19, Apr. 2008.