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Quasi-continuous function : ウィキペディア英語版
Quasi-continuous function
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.
==Definition==

Let X be a topological space. A real-valued function f:X \rightarrow \mathbb is quasi-continuous at a point x \in X if for any every \epsilon > 0 and any open neighborhood U of x there is a non-empty open set G \subset U such that
: |f(x) - f(y)| < \epsilon \;\;\;\; \forall y \in G
Note that in the above definition, it is not necessary that x \in G .

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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