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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Pseudo-boundaries and pseudo-interiors in Euclidean spaces and topological manifolds


Authors: Ross Geoghegan and R. Richard Summerhill
Journal: Trans. Amer. Math. Soc. 194 (1974), 141-165
MSC: Primary 57A15
MathSciNet review: 0356061
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Abstract: The negligibility theorems of infinite-dimensional topology have finite-dimensional analogues. The role of the Hilbert cube $ {I^\omega }$ is played by euclidean n-space $ {E^n}$, and for any nonnegative integer $ k < n$, k-dimensional dense $ {F_\sigma }$-subsets of $ {E^n}$ exist which play the role of the pseudo-boundary of $ {I^\omega }$. Their complements are $ (n - k - 1)$-dimensional dense $ {G_\delta }$ pseudo-interiors of $ {E^n}$. Two kinds of k-dimensional pseudo-boundaries are constructed, one from universal compacta, the other from polyhedra. All the constructions extend to topological manifolds.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0356061-0
PII: S 0002-9947(1974)0356061-0
Article copyright: © Copyright 1974 American Mathematical Society