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Full-Text Articles in Mathematics
Left-Separation Of Ω1, Lukas Stuelke, Adrienne Stanley Ph.D.
Left-Separation Of Ω1, Lukas Stuelke, Adrienne Stanley Ph.D.
Summer Undergraduate Research Program (SURP) Symposium
A topological space is left-separated if it can be well-ordered so that every initial segment is closed. Here, we show that all countable ordinal numbers are left-separated. We then prove that a similar method could not work for ω1 , using the pressing-down lemma1 . We finish by showing that a left-separating well-ordering on ω1 necessarily leads to a contradiction.
Rendezvous Numbers Of Compact And Connected Spaces, Kevin Demler, Bill Wood Ph.D.
Rendezvous Numbers Of Compact And Connected Spaces, Kevin Demler, Bill Wood Ph.D.
Summer Undergraduate Research Program (SURP) Symposium
The concept of a rendezvous number was originally developed by O. Gross in 1964, and was expanded upon greatly by J. Cleary, S. Morris, and D. Yost in 1986. This number exists for every metric space, yet very little is known about it, and it’s exact value for most spaces is not known. Furthermore, it’s exact value is difficult to calculate, and in most cases we can only find bounds for the value. We focused on their arguments using convexity and applied it to shapes in different metrics and graphs. Using sets of points that stood out (vertices, midpoints) as …