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


Authors: J. J. Dijkstra, J. van Mill and J. Mogilski
Journal: Trans. Amer. Math. Soc. 332 (1992), 693-709
MSC: Primary 57N20; Secondary 54F65, 57N15
DOI: https://doi.org/10.1090/S0002-9947-1992-1052905-9
MathSciNet review: 1052905
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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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DOI: https://doi.org/10.1090/S0002-9947-1992-1052905-9
Article copyright: © Copyright 1992 American Mathematical Society

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