منابع مشابه
A Proof of the Jordan Curve Theorem
Let F be a Jordan curve in the plane, i.e. the image of the unit circle C = {(x,y);x + y = 1} under an injective continuous mapping y into R. The Jordan curve theorem [1] says that / ? 2 \ F is disconnected and consists of two components. (We shall use the original definition whereby two points are in the same component if and only if they can be joined by a continuous path (image of [0,1]).) A...
متن کاملJordan’s Proof of the Jordan Curve Theorem
This article defends Jordan’s original proof of the Jordan curve theorem. The celebrated theorem of Jordan states that every simple closed curve in the plane separates the complement into two connected nonempty sets: an interior region and an exterior. In 1905, O. Veblen declared that this theorem is “justly regarded as a most important step in the direction of a perfectly rigorous mathematics”...
متن کاملThe Jordan Curve Theorem, Formally and Informally
1. INTRODUCTION. The Jordan curve theorem states that every simple closed pla-nar curve separates the plane into a bounded interior region and an unbounded exterior. One hundred years ago, Oswald Veblen declared that this theorem is " justly regarded as a most important step in the direction of a perfectly rigorous mathematics " [13, p. 83]. Its position as a benchmark of mathematical rigor has...
متن کاملThe Jordan curve theorem is non - trivial
The formal mathematical definition of a Jordan curve (a non-self-intersecting continuous loop in the plane) is so simple that one is often lead to the unimaginative view that a Jordan curve is nothing more than a circle or an ellipse. In this paper, we continue a discussion of others [1, 2, 9, 11] that a Jordan curve can be quite fantastical both in some bizarre properties such a curve might ha...
متن کاملGroupoids, the Phragmen-brouwer Property, and the Jordan Curve Theorem
We publicise a proof of the Jordan Curve Theorem which relates it to the Phragmen-Brouwer Property, and whose proof uses the van Kampen theorem for the fundamental groupoid on a set of base points.
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1975
ISSN: 0035-7596
DOI: 10.1216/rmj-1975-5-2-225