Cancellation of 3-Point Topological 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.
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
Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Universitat Politècnica de València
e-ISSN: 1989-4147 https://doi.org/10.4995/agt