The proof of

Some other related links: 1, 2, 3, 4.Jordan curve theorem- the theorem that states that every simple closed curve divides a plane into two parts and is the common boundary between them (see The American Heritage Dictionary of the English Language).

This theorem seems quite obvious, however it is common knowledge that it is very difficult to it prove rigorously. Mizar formalization follows the script

with the property that ordinates of points in the same column are equal as well as abscissae of points in rows and, moreover,

(x _{1},y_{1})... (x _{1},y_{n})... ... ... (x _{n},y_{1})... (x _{n},y_{n})

Together with several subsequent articles devoted to further development of the theory ofEvery two special arcs lying in a rectangleRsuch that the first arc joins the upper and lower sides ofRand the second arc joins the left and right sides ofRhave a non empty intersection.

The preliminary work on the proof of general

[ Home | Project | Language | System | People | MML | FM | SUM ]

Last modified: January 21, 2003