Non-separating immersions of spheres and Bing houses

TL;DR

This paper constructs Bing houses in all dimensions greater than or equal to three, providing non-separating piecewise-linear immersions of spheres into Euclidean spaces of one higher dimension.

Contribution

It introduces a method to create Bing houses in all dimensions, enabling non-separating PL immersions of spheres into Euclidean spaces.

Findings

Bing houses constructed in all dimensions n ≥ 3

Non-separating PL immersions of spheres achieved

Extension of Bing house theory to higher dimensions

Abstract

We construct Bing houses in all dimensions $n \geq 3$, obtaining non-separating PL immersions of $\mathbb{S}^n \rightarrow\mathbb{R}^{n+1}$.