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# Tag Archives: Brouwer’s Fixed Point Theorem

## Around Jordans Curve Theorem I

There are more or less three theorems that are often called Jordan Curve Theorems, while there is a distinction between them. Let us denote by E the Euclidean plane, [tex]E=\mathbb{R}^2[/tex] and by [tex]E^n[/tex] the Euclidean n-dimensional space, [tex]E^n=\mathbb{R}^n[/tex]. The Jordan … Continue reading

Posted in Mathematics, Topology
Tagged Brouwer's Fixed Point Theorem, Jodan's Curve Theorem
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## Even More On BFPT

I wouldn’t mind writing this unless I haven’t already posted two different proofs of Brouwer’s Fixed Point Theorem. Namely a friend of mine and a reader of this blog, exposed me to another way of proving it. This proof has … Continue reading

## Games in Topology (Another Proof of Brouwer’s Fixed Point Theorem)

Theorem (Brouwer’s Fixed Point Theorem, BFPT). Suppose that [tex]B\subset \mathbb{R}^n[/tex] is the closed n-dimensional unit ball and [tex]f\colon B\to B[/tex] is a continuous function. Then there exists a point [tex]x\in B[/tex] such that [tex]f(x)=x[/tex]. Theorem (Jordan’s Curve Theorem) Let [tex]f\colon … Continue reading

Posted in Combinatorics, Games, Mathematics, Topology
Tagged Brouwer's Fixed Point Theorem
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## Brouwer’s Fixed Point Theorem: Many in One Post

In this post I will (1) give a simple proof of Brouwer Fixed Point Theorem (2) fulfill the promise given here (3) present the Wednesday Problem in the form fill in the details in the below text Theorem (Brouwer’s Fixed … Continue reading

Posted in Combinatorics, Mathematics, Topology, Wednesday Problem
Tagged Brouwer's Fixed Point Theorem
2 Comments