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A cancellation law for partially ordered sets and $T_0$ spaces

Author(s): B. Banaschewski; R. Lowen
Journal: Proc. Amer. Math. Soc. 132 (2004), 3463-3466.
MSC (2000): Primary 06A06, 54B10
Posted: July 22, 2004
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Abstract: In this paper we prove a cancellation law in the category (1) of partially ordered sets and (2) of $T_0$ spaces, the respective conditions on the common factor being that it have (1) an irreducible bottom element and (2) an irreducible bottom element in its specialization order.

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Behrends E. and Pelant J. The cancellation law for compact Hausdorff spaces and vector-valued Banach-Stone theorems Arch. Math. 64 (1995) 341-343 MR 1319005 (96h:46046)

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Borsuk K. Sur la décomposition des polyèdres en produits cartésiens Fund. Math. 33 (1938) 137-148

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Fox R.H. On a problem of S. Ulam concerning cartesian products Fund. Math. 34 (1947) 278-287 MR 0027502 (10:316a)

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Zeron S.E. Cancellation laws in topological products Houston J. Math. 27 (2001) 67-74 MR 1843913 (2002d:54003)

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Additional Information:

B. Banaschewski
Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1

R. Lowen
Affiliation: Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, 2020 Antwerp, Belgium
Email: rlow@ruca.ua.ac.be

DOI: 10.1090/S0002-9939-04-07339-3
PII: S 0002-9939(04)07339-3
Keywords: Cancellation, product, partially ordered set, $T_0$ space, specialization order.
Received by editor(s): September 26, 2002
Received by editor(s) in revised form: May 7, 2003
Posted: July 22, 2004
Communicated by: Alan Dow
Copyright of article: Copyright 2004, American Mathematical Society

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