The uniform limit theorem concerns a sequence of functions with this property and is proven using an epsilon-over-three argument.
Poset functions with the Scott form of this property preserve directed suprema (soo-PREE-mah). A function has this property if its oscillation at each point is zero. In topology, a function has this property if its inverse takes open sets to open sets. The uniform limit theorem concerns a sequence of functions with this property and is proven using an epsilon-over-three argument. The topologist's sine curve lacks this property when x is zero, and the Weierstrass (VYE-er-shtross) function has this property everywhere despite being nowhere differentiable. A function f has this property at a if the limit, as x approaches a, of f-of-x, equals f-of-a. For 10 points, identify this property of functions that lack jumps, holes, and vertical asymptotes.
Poset functions with the Scott form of this property preserve directed suprema (soo-PREE-mah).
continuity [or continuous] &lt;Thompson&gt;