Separation in Spaces and Hyperspaces

Presenters

Jonathan Proctor, Cedarville University

Type of Submission

Poster

Campus Venue

Dixon Ministry Center, Alumni Hall

Location

Cedarville, OH

Start Date

4-10-2013 1:00 PM

End Date

4-10-2013 5:00 PM

Comments

Abstract:

This poster describes the topological relationships between the separation of a space and the separation of its hyperspace under the Vietoris topology. In particular, we focus on the first four separation properties in both the space and the hyperspace. We found that many separation properties of the original space will transfer to the hyperspace, but very few of the separation properties of the hyperspace transfer back to the original space. With some basic assumptions about the separation of the original space, we found that more of the separation properties of the hyperspace can be transferred back to the original space. We provide proofs of all of these results, and we also present counterexamples to demonstrate that these relationships are as strong as they can be in the general case.

Creative Commons License

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