Classification of finite-dimensional universal pseudo-boundaries and pseudo-interiors

Dijkstra, J. J.; van Mill, J.; Mogilski, J.

doi:10.1090/S0002-9947-1992-1052905-9

Classification of finite-dimensional universal pseudo-boundaries and pseudo-interiors
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by J. J. Dijkstra, J. van Mill and J. Mogilski PDF

Trans. Amer. Math. Soc. 332 (1992), 693-709 Request permission

Abstract:

Let $n$ and $k$ be fixed integers such that $n \geq 1$ and $0 \leq k \leq n$. Let $B_k^n$ and $s_k^n$ denote the $k$-dimensional universal pseudo-boundary and the $k$-dimensional universal pseudo-interior in ${{\mathbf {R}}^n}$, respectively. The aim of this paper is to prove that $B_k^n$ is homeomorphic to $B_k^m$ if and only if $s_k^n$ is homeomorphic to $s_k^m$ if and only if $n = m$ or $n$, $m \geq 2k + 1$.

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