Cancellation of 3-Point Topological Spaces
Submitted: 2013-11-12
|Accepted: 2013-11-12
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Keywords:
Homeomorphism, Cancellation problem, 3-point spaces
Supporting agencies:
Funda¸c˜ao para a Ciˆencia e Tecnologia (Portugal)
Abstract:
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.
References:
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.
