Closed infinite broom: Difference between revisions
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==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 <math>(0,0)</math> to <math>(1,0)</math>, and the line segment joining <math>(0,0)</math> to <math>(1,1/n)</math> where <math>n</math> varies over the natural numbers. | |||
[[File:Closedinfinitebroom.png|350px]] | |||
Latest revision as of 00:08, 21 December 2010
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.
