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

be a topological space and any open neighborhood there is a non-empty open set such that

.

Properties

• is quasi-continuous

• is quasi-continuous.

Example

thus f is quasi-continuous.

is a rational number is an irrational number.

See also

• Cliquish function

References