Тhe concept of topological well-ordered space
Abstract
UDC 515.12
Since the general definition of topology is based on the characteristics of the standard Euclidean topology, the relationships between the ordering on real numbers and its topology have been generalized over time and studied in numerous aspects. The compatibility of partially ordered sets with the topology on them was studied by many researchers. On the other hand, well-orderedness is an important concept of the set theory. We define the concept of topological well-orderedness, which can be regarded as a topological generalization of well-orderedness in the set theory, and analyze its basic properties. In this way, the relationship between well-orderedness and topology is established from a different point of view. Finally, some basic applications of the concept of topological well-orderedness to the graph theory are investigated.
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