The Heine-Cantor theorem states that if there is compactness, this property is equivalent to its uniform variety. The Dirichlet function does not have this property anywhere. In Lesbegue integration, its absolute version holds for a function f on an interval if and only if there exists a function g such that the integral of g from the start of the interval to any point in the interval equals f. Its topological definition 
The Heine-Cantor theorem states that if there is compactness, this property is equivalent to its uniform variety. The Dirichlet function does not have this property anywhere. In Lesbegue integration, its absolute version holds for a function f on an interval if and only if there exists a function g such that the integral of g from the start of the interval to any point in the interval equals f. Its topological definition requires that the inverse of every open set be open.  A function f of x has this property at a point b if the limit of f of x as x approaches b is f of b. For 10 points, name this property of some functions, sometimes described as the ability to be drawn without raising a pencil.
The Heine-Cantor theorem states that if there is compactness, this property is equivalent to its uniform variety.
continuous [accept word forms]