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Title: Continuous Function -- from Wolfram MathWorld

Open Graph Title: Continuous Function -- from Wolfram MathWorld

X Title: Continuous Function -- from Wolfram MathWorld

Description: There are several commonly used methods of defining the slippery, but extremely important, concept of a continuous function (which, depending on context, may also be called a continuous map). The space of continuous functions is denoted C^0, and corresponds to the k=0 case of a C-k function. A continuous function can be formally defined as a function f:X->Y where the pre-image of every open set in Y is open in X. More concretely, a function f(x) in a single variable x is said to be...

Open Graph Description: There are several commonly used methods of defining the slippery, but extremely important, concept of a continuous function (which, depending on context, may also be called a continuous map). The space of continuous functions is denoted C^0, and corresponds to the k=0 case of a C-k function. A continuous function can be formally defined as a function f:X->Y where the pre-image of every open set in Y is open in X. More concretely, a function f(x) in a single variable x is said to be...

X Description: There are several commonly used methods of defining the slippery, but extremely important, concept of a continuous function (which, depending on context, may also be called a continuous map). The space of continuous functions is denoted C^0, and corresponds to the k=0 case of a C-k function. A continuous function can be formally defined as a function f:X->Y where the pre-image of every open set in Y is open in X. More concretely, a function f(x) in a single variable x is said to be...

Opengraph URL: https://mathworld.wolfram.com/ContinuousFunction.html

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DC.TitleContinuous Function
DC.CreatorWeisstein, Eric W.
DC.DescriptionThere are several commonly used methods of defining the slippery, but extremely important, concept of a continuous function (which, depending on context, may also be called a continuous map). The space of continuous functions is denoted C^0, and corresponds to the k=0 case of a C-k function. A continuous function can be formally defined as a function f:X->Y where the pre-image of every open set in Y is open in X. More concretely, a function f(x) in a single variable x is said to be...
DC.Subject30A
DC.RightsCopyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement.
DC.Formattext/html
DC.Identifierhttps://mathworld.wolfram.com/ContinuousFunction.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
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Continuously Differentiable Functionhttps://mathworld.wolfram.com/ContinuouslyDifferentiableFunction.html
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Piecewise Continuoushttps://mathworld.wolfram.com/PiecewiseContinuous.html
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Introduction to Real Analysis.http://www.amazon.com/exec/obidos/ASIN/0471510009/ref=nosim/ericstreasuretro
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