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jk22
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I ask this for the condition of application of Stoke's theorem.
A closed knot is a mathematical concept that refers to a continuous loop formed by a curve or line in three-dimensional space. It can also be thought of as a closed loop with no loose ends or endpoints.
The boundary of a surface is the edge or border that separates the surface from its surroundings. In the case of a closed knot, the boundary would be the knot itself.
Yes, it is possible for a surface to have a closed knot as its boundary. This is a common topic of study in topology, which is the branch of mathematics that deals with the properties of geometric objects that are preserved through continuous deformations.
One example is a Möbius strip, which is a one-sided surface with a closed knot as its boundary. Another example is a torus, which is a doughnut-shaped surface with a closed knot as its boundary.
The study of these surfaces has important applications in various fields such as physics, biology, and engineering. It also helps us understand the fundamental properties of surfaces and their boundaries, which can lead to new discoveries and advancements in mathematics and other sciences.