@article{Kandemir_Uludağ_2023, title={Тhe concept of topological well-ordered space}, volume={75}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/7145}, DOI={10.37863/umzh.v75i6.7145}, abstractNote={<p>UDC 515.12</p> <p>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.<span class="Apple-converted-space"> </span>The compatibility of partially ordered sets with the topology on them was<span class="Apple-converted-space"> </span>studied by many researchers.<span class="Apple-converted-space"> </span><span class="Apple-converted-space"> </span>On the other hand, well-orderedness is an important concept of the set theory.<span class="Apple-converted-space"> </span>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.<span class="Apple-converted-space"> </span>In this way, the relationship between well-orderedness and topology is<span class="Apple-converted-space"> </span>established from a different point of view.<span class="Apple-converted-space"> </span>Finally, some basic applications of the concept of topological<span class="Apple-converted-space"> </span>well-orderedness to the graph theory are investigated.</p>}, number={6}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={KandemirMustafa Burç and UludağDilan Başak}, year={2023}, month={Jun.}, pages={817 - 829} }