An Inverse System of Nonempty Objects with Empty Limit

TL;DR

This paper provides a specific example of an inverse system of nonempty sets with onto bonding maps whose inverse limit is empty, illustrating a counterintuitive phenomenon in topology.

Contribution

It introduces an explicit inverse system with nonempty objects and onto bonding maps that results in an empty inverse limit, highlighting a novel topological construction.

Findings

Counterexample to inverse limit intuition

Explicit construction of inverse system with empty limit

Insights into inverse system properties

Abstract

In this article we give an explicit example of an inverse system with nonempty sets and onto bonding maps such that its inverse limit is empty.