Pseudo-Boundaries and Pseudo-Interiors in Euclidean Spaces and Topological Manifolds
Pseudo-Boundaries and Pseudo-Interiors in Euclidean Spaces and Topological Manifolds
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 …