Concerning $n$-mutual aposyndesis in products of continua
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- by Leland E. Rogers PDF
- Trans. Amer. Math. Soc. 162 (1971), 239-251 Request permission
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 βsuper n-mutually aposyndeticβ continuum) with every compact Hausdorff continuum is n-mutually aposyndetic for each $n \geqq 2$.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 162 (1971), 239-251
- MSC: Primary 54F15
- DOI: https://doi.org/10.1090/S0002-9947-1971-0293599-6
- MathSciNet review: 0293599