Problem of multiple generality - Revision history

en>John of Reading: Typo fixing, replaced: alloted → allotted using AWB

2015-01-09T13:11:02Z

Typo fixing, replaced: alloted → allotted using AWB

en>Addbot: Bot: Migrating 2 interwiki links, now provided by Wikidata on d:q7246960

2013-03-23T03:39:25Z

Bot: Migrating 2 interwiki links, now provided by Wikidata on d:q7246960

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+In [[mathematics]], the notion of a '''quasi-continuous function''' is similar to, but weaker than, the notion of a [[continuous function]].  All continuous functions are quasi-continuous but the converse is not true in general.
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+==Definition==
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+Let <math> X </math> be a [[topological space]].  A real-valued function <math> f:X \rightarrow \mathbb{R} </math> is quasi-continuous at a point <math> x \in X </math> if for any every <math> \epsilon > 0 </math> and any [[open neighborhood]] <math> U </math> of <math> x </math> there is a non-empty [[open set]] <math> G \subset U </math> such that
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+: <math>  |f(x) - f(y)| < \epsilon \;\;\;\; \forall y \in G </math>
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+Note that in the above definition, it is not necessary that <math> x \in G </math>.
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+==Properties==

150.161.2.200 at 16:56, 27 June 2012

2012-06-27T16:56:47Z

New page

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