Osgood Curve
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, an Osgood curve is a Jordan curve of positive area. The first example was found by Osgood (1903). Examples of Osgood curves can be produced by slightly modifying one of the constructions of space-filling curves with image the unit square to make it an embedding, though the cost is that it no longer fills the whole unit square. In topology, the Jordan curve theorem states that every non-self-intersecting loop in the plane (also known as a Jordan curve) ...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, an Osgood curve is a Jordan curve of positive area. The first example was found by Osgood (1903). Examples of Osgood curves can be produced by slightly modifying one of the constructions of space-filling curves with image the unit square to make it an embedding, though the cost is that it no longer fills the whole unit square. In topology, the Jordan curve theorem states that every non-self-intersecting loop in the plane (also known as a Jordan curve) divides the plane into an "inside" and an "outside" region, and any path connecting a point of one region to a point of the other intersects that loop somewhere. The first to give a proof was Camille Jordan (1887). It has generally been thought that his proof was flawed and that Veblen (1905) gave the first rigorous proof, but this view has been disputed by Hales (2007b).
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