TITLE:
A Basic Topological Approach to the Continuity of the Size Function
AUTHORS:
François Dubeau
KEYWORDS:
Size Function, Connexity, Path, Calm Set, Measure Function
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.12 No.10,
October
26,
2022
ABSTRACT: We present old and new results about the size function of a set providing simple and complete proofs using basic tools of general topology. For instance, the decomposition of the size function is given and, under the calmness property of a set, the right continuity of the size function with respect to both arguments is established. Finally, a classification of its points of discontinuity is given.