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Topology on Semi-Well Ordered Sets

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A semi-well ordered set is a partially ordered set in which every non-empty subset of it contains a least element or a greatest element. It is defined as an extension of the concept of well ordered sets. An attempt is made to identify the properties of a semi-well ordered set equipped with the order topology.

Abstract

A semi-well ordered set is a partially ordered set in which every non-empty subset of it contains a least element or a greatest element. It is defined as an extension of the concept of well ordered sets. An attempt is made to identify the properties of a semi-well ordered set equipped with the order topology.

참고문헌 (18)

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  12. P.T, Ramachandran, "Some problems in set topology relating group, homeomorphisms and order", Ph.D., pp.1985
  13. D. Schmidt, "The relation between the height of a well-founded partial ordering and the order types of its chains and antichains", J. Combin. Theory Ser. B, 31(2), pp.183~189 (1981)
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  16. Sunny, Angela, "Semi-well ordered sets and semi-ordinals, communicated", ~
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  18. E. S. Wolk, "Topology on a partially well ordered set", Fund. Math., 62, pp.255~264 (1968)

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