Quips about the Jordan curve theorem aside, I don't think that's really a meaningful question. It is or it isn't, depending on how you want to model it.
Yield curves are bootstrapped from known bond yields at liquidly-traded tenors (1Y, 2Y, 5Y, 10Y, and short-dated). Those are the heavy black dots in the image. Outside of those tenors the 'true' rate is anyone's guess: you're basically interpolating. Whether that interpolation is continuous is up to you!
Yield curves are bootstrapped from known bond yields at liquidly-traded tenors (1Y, 2Y, 5Y, 10Y, and short-dated). Those are the heavy black dots in the image. Outside of those tenors the 'true' rate is anyone's guess: you're basically interpolating. Whether that interpolation is continuous is up to you!