eduzhai > Applied Sciences > Computer Science >

On an Extension of a Theorem of Eilenberg and a Characterization of Topological Connectedness

  • KanKan
  • (0) Download
  • 20210425
  • Save

... pages left unread,continue reading

Document pages: 11 pages

Abstract: On taking a non-trivial and semi-transitive bi-relation constituted by two(hard and soft) binary relations, we report a (i) p-continuity assumption thatguarantees the completeness and transitivity of its soft part, and a (ii)characterization of a connected topological space in terms of its attendantproperties on the space. Our work generalizes antecedent results in appliedmathematics, all following Eilenberg (1941), and now framed in the context of aparametrized-topological space. This re-framing is directly inspired by thecontinuity assumption in Wold (1943-44) and the mixture-space structureproposed in Herstein and Milnor (1953), and the unifying synthesis of thesepioneering but neglected papers that it affords may have independent interest.

Please select stars to rate!

         

0 comments Sign in to leave a comment.

    Data loading, please wait...
×