A separable non-remainder of H

TL;DR

This paper demonstrates, under certain set-theoretic assumptions, the existence of a compact separable continuum that cannot be realized as a remainder of the real line, challenging previous assumptions about remainders.

Contribution

It establishes the consistent existence of a compact separable continuum not being a remainder of the real line, providing new insights into the structure of remainders.

Findings

Existence of such a continuum is consistent with set theory.

Challenges previous beliefs about remainders of the real line.

Provides a new perspective on the topology of remainders.

Abstract

We prove that there is a compact separable continuum that (consistently) is not a remainder of the real line.