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

Geoghegan, Ross; Summerhill, R. Richard

doi:10.1090/S0002-9947-1974-0356061-0

Pseudo-boundaries and pseudo-interiors in Euclidean spaces and topological manifolds
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by Ross Geoghegan and R. Richard Summerhill PDF

Trans. Amer. Math. Soc. 194 (1974), 141-165 Request permission

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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