These functions are defined as ones for which the preimage of open sets are open and the function must be one on a closed interval in the extreme, mean, and intermediate value theorems.
These functions are the morphisms in the category Top. A surjective function of this kind that evenly covers a neighborhood of every image point is called a covering map. There exists a sequence of polynomials converging uniformly to any of these functions by the Stone-Weierstrass theorem. By an epsilon-over-3 argument, if a sequence of them converges uniformly, then the limit is one of these functions as well. These functions preserve (*) compactness and connectedness. These functions are defined as ones for which the preimage of open sets are open and the function must be one on a closed interval in the extreme, mean, and intermediate value theorems. For 10 points, name these functions where f of cequals the limit of f of x as x approaches c. 
These functions are the morphisms in the category Top. A surjective function of this kind that evenly covers a neighborhood of every image point is called a covering map.
continuous function