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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Concerning $ n$-mutual aposyndesis in products of continua


Author: Leland E. Rogers
Journal: Trans. Amer. Math. Soc. 162 (1971), 239-251
MSC: Primary 54F15
MathSciNet review: 0293599
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Abstract: This paper is concerned with Cartesian products of regular Hausdorff continua and certain conditions on the factors that make the product n-mutually aposyndetic (given n distinct points, there are n disjoint subcontinua, each containing one of the points in its interior). It is proved that the product of any three regular Hausdorff continua is n-mutually aposyndetic for each $ n \geqq 2$. Next, certain conditions on factors of products of two continua are shown to be sufficient for the product to be n-mutually aposyndetic. In connection with this, the concepts of n-semiaposyndesis and aposyndetic-terminal points are introduced. Finally, it is proved that the product of a simple closed curve (or any other ``super n-mutually aposyndetic'' continuum) with every compact Hausdorff continuum is n-mutually aposyndetic for each $ n \geqq 2$.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0293599-6
Keywords: Aposyndetic continuum, aposyndesis, mutual aposyndesis, semiaposyndesis, terminal point, Cartesian product
Article copyright: © Copyright 1971 American Mathematical Society