# Closed infinite broom

From Topospaces

This article describes a standard counterexample to some plausible but false implications. In other words, it lists a pathology that may be useful to keep in mind to avoid pitfalls in proofs

View other standard counterexamples in topology

## Definition

The **closed infinite broom** is the subset of the Euclidean plane obtained as the union of the following line segments: the line segment joining to , and the line segment joining to where varies over the natural numbers.