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👉 The term "nondegenerate" is a mathematical concept in functional analysis and topology. It refers to a set that satisfies certain properties, but does not contain any closed sets or singular points. In the context of mathematics, it can be used to describe a topological space where every point has a neighborhood that contains no isolated points (i.e., it has "nondegenerate" neighborhoods). This property ensures that the topology is well-behaved and allows for operations like compactness and separation ax

nondegenerately

👉 In mathematics and physics, a non-degenerate function is a function that has at least one real root. In other words, it is defined on an open interval containing the roots of its derivative and does not have any singularities in that domain. Non-degeneracy refers to the fact that a function cannot be identically zero or undefined at any point where the function itself could potentially be discontinuous or non-continuous. This means that if a function has a non-zero derivative, it must also

nondegenerate

👉 In mathematics, a set of numbers is called non-degenerate if it does not contain any two distinct elements that are equal. This means that the set can have one or more elements that are equal to each other, but no element can be equal to itself (i.e., if x = y then z = w). A set that meets this condition is said to be nondegenerate.

nondegenerateness