Fixed point and non-retract theorems -- classical circular tours (Q5935719)
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scientific article; zbMATH DE number 1610929
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fixed point and non-retract theorems -- classical circular tours |
scientific article; zbMATH DE number 1610929 |
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Fixed point and non-retract theorems -- classical circular tours (English)
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19 August 2002
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The authors describe a circular tour by recalling the fact (by now known to each undergraduate) that each of the following results can be used to give a simple proof of the following one: Brouwer's fixed point theorem \(\Rightarrow\) Sperner's lemma \(\Rightarrow\) KKM theorem \(\Rightarrow\) Brouwer's fixed point theorem. Finally, they derive the usual corollaries.
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Brouwer's fixed point theorem
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Sperner's lemma
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KKM theorem
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