Characteristic spaces emerging from primitive chaos

This paper describes the emergence of two characteristic notions, nondegenerate Peano continuum and Cantor set, by the exploration of the essence of the existence of primitive chaos from a topological viewpoint. The primitive chaos is closely related to vital problems in physics itself and leads to chaotic features under natural conditions. The nondegenerate Peano continuum represents an ordinarily observed space, and the existence of a single nondegenerate Peano continuum guarantees the existence of infinite varieties of the primitive chaos leading to the chaos. This result provides an explanation of the reason why we are surrounded by diverse chaotic behaviors. Also, the Cantor set is a general or universal notion different from the special set, the Cantor middle-third set, and the existence of a single Cantor set guarantees infinite varieties of the primitive chaos leading to the chaos. This analogy implies the potential of the Cantor set for the method of new recognizing physical phenomena.