Cancellation of 3-Point Topological Spaces

Abstract

The cancellation problem, which goes back to S. Ulam [2], 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 [1] 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 [4].