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

Abstract

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