These functions on a closed interval can be uniformly approximated by polynomials by the (*) Stone-Weierstrass theorem.
By the Heine-Cantor theorem, every function of this kind between a compact metric space and a metric space possesses the uniform version of this property. These functions on a closed interval can be uniformly approximated by polynomials by the (*) Stone-Weierstrass theorem. A function of this kind on a closed interval will attain all intermediate values, and all differentiable functions have this property. For functions with this property, f of a equals the limit of f of x as x approaches a, meaning the function has no "holes" or "jumps." For 10 points, name this property describing functions you can draw without lifting your pencil from the paper.
By the Heine-Cantor theorem, every function of this kind between a compact metric space and a metric space possesses the uniform version of this property.
continuous (accept word forms like “continuity”)