Cancellation of 3-Point Topological Spaces

Sheila Carter, F.J. Craveiro de Carvalho


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.


Homeomorphism; Cancellation problem; 3-point spaces

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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.

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1. Some further results on the cancellation law for partially ordered sets and T0-spaces
Jing Liu, Shengwei Han
Topology and its Applications  vol: 300  first page: 107765  year: 2021  
doi: 10.1016/j.topol.2021.107765

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