Equivalence classes are subsets formed by grouping elements that are equivalent under a given relation, meaning that each element in a class is related to every other element in that same class. This concept helps in understanding how different objects can be seen as the same under specific transformations, especially when dealing with knots and their representations. In knot theory, equivalence classes can help classify knots based on whether they can be transformed into one another through specific operations like planar and regular isotopy.
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