Topologist's sine curve

The Topologist's sine curve is a classic example from topology and real analysis that illustrates the concept of convergence and the properties of compact spaces. It is defined as the closure of the set of points in the Cartesian plane given by the parametric equations: \[ (x, \sin(1/x)) \text{ for } x > 0. \] The sine curve oscillates between -1 and 1 as \( x \) approaches 0 from the right.