JORDAN CURVE THEOREM Meaning and
Definition
-
The Jordan curve theorem is a fundamental result in topology that addresses the properties of a closed simple curve in a plane. According to this theorem, any simple closed curve in a plane divides the plane into two disjoint regions, one bounded and the other unbounded. These regions are commonly referred to as the inside and outside of the curve.
Formally, the Jordan curve theorem states that if a curve is homeomorphic to a circle, it is also homeomorphic to the unit circle. In simpler terms, this means that any closed curve without self-intersections is essentially the same as a circle in terms of its topological properties.
The significance of the Jordan curve theorem lies in its ability to classify and distinguish between different types of curves. It provides a way to identify closed curves and determine their interior and exterior regions. This theorem plays a crucial role in different areas of mathematics, such as complex analysis and geometric topology, where understanding the properties and behavior of curves is essential.
Overall, the Jordan curve theorem offers a foundational understanding of the relationship between curves and their surrounding space, enabling mathematicians to analyze and study complex shapes and structures, and making it an integral part of topological theory.
Common Misspellings for JORDAN CURVE THEOREM
- hordan curve theorem
- nordan curve theorem
- mordan curve theorem
- kordan curve theorem
- iordan curve theorem
- uordan curve theorem
- jirdan curve theorem
- jkrdan curve theorem
- jlrdan curve theorem
- jprdan curve theorem
- j0rdan curve theorem
- j9rdan curve theorem
- joedan curve theorem
- joddan curve theorem
- jofdan curve theorem
- jotdan curve theorem
- jo5dan curve theorem
- jo4dan curve theorem
- jorsan curve theorem
- jorxan curve theorem
