Hausdorff dimension of continuous functions with at most finite UV points on closed intervals
In this paper, we present a new method to investigate continuous functions with at most finite unbounded variation points on closed intervals. We need to point out that, although the issue is interesting in the prior investigations, the new method should be emphasized. Using this method, Hausdorff dimension of any continuous functions with one unbounded variation point on closed intervals is 1 has been given. Furthermore, definition of unbounded variation point has been given. In the end, if unbounded variation point is at most finite, corresponding conclusion still holds.