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discontinuous

Encyclopedia

In topology and related branches of mathematics, an action of a group G on a topological space X is called properly discontinuous if every element of X has a neighborhood that moves outside itself under the action of any group element but the trivial element. — “Properly discontinuous action - Wikipedia, the free encyclopedia”, en.wikipedia.org

Consider a real valued function ƒ of a real variable x, defined in a neighborhood of the point x0 in which ƒ is discontinuous. Thomae's function is discontinuous at every rational point, but continuous at every irrational point. — “Classification of discontinuities - Wikipedia, the free”, en.wikipedia.org

It turns out that for maps defined on infinite-dimensional topological vector spaces (e.g., infinite-dimensional normed spaces), the answer is generally no: there exist discontinuous linear maps. Examples of discontinuous linear maps are easy to construct in spaces. — “Discontinuous linear map - Wikipedia, the free encyclopedia”, en.wikipedia.org

Quotations

Laws of motion of any kind become comprehensible to man only when he examines arbitrarily selected elements of that motion; but at the same time, a large proportion of human error comes from the arbitrary division of continuous motion into discontinuous elements. — “War and Peace” by Leo Tolstoy

Laws of motion of any kind become comprehensible to man only when he examines arbitrarily selected elements of that motion; but at the same time, a large proportion of human error comes from the arbitrary division of continuous motion into discontinuous elements. — “War and Peace” by Leo Tolstoy

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