On level sets of a continuous nowhere monotone function

An Analysis of Katsuura’s Continuous Nowhere Differentiable Function

A Continuous Skeletonization Method Based on Level Sets

A robust and efficient method in 2D and 3D for the calculation of skeletons for arbitrary objects is presented. The method is based on the calculation of the distance function with respect to the object boundary. This is combined, in a post processing step, with a new indicator to identify the skeleton, which coincides with the singularity set of the distance map. The indicator is defined as a ...

Insertion of a gamma-continuous function

A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

Everywhere Continuous Nowhere Differentiable Functions

Here I discuss the use of everywhere continuous nowhere differentiable functions, as well as the proof of an example of such a function. First, I will explain why the existence of such functions is not intuitive, thus providing significance to the construction and explanation of these functions. Then, I will provide a specific detailed example along with the proof for why it meets the requireme...

Positive sets and monotone sets

In this paper, we show how convex analysis can be applied to the theory of sets that are “positive” with respect to a continuous quadratic form on a Banach space. Monotone sets can be considered as a special case of positive sets, and we show how our results lead to very efficient proofs of a number of results on monotone sets. One of the key techniques that we use is a generalization of the Fi...