View Proposal #298
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ID | 298 |
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First Name | Luke |
Last Name | Serafin |
Institution | Coe College |
Speaker Category | undergraduate student |
Title of Talk | Explicit Constructions of Functions whose Graphs are Dense in The Plane |
Abstract | A set D is dense in the plane if and only if every open ball in the plane contains an element of D. We prove that there exists a function f from the real line R to itself whose graph is dense in the plane by explicitly constructing it using a partition of the rationals into countably many subsets dense in R. We then use this method of construction to prove that there are 2^(2^\aleph_0) functions whose graphs are dense in the plane, and that there exists a function f: R ->R such that f(U) = R for every non-empty open set U in R. |
Subject area(s) | |
Suitable for undergraduates? | Yes |
Day Preference | |
Computer Needed? | |
Bringing a laptop? | Y |
Overhead Needed? | |
Software requests | |
Special Needs | |
Date Submitted | 10/17/2010 |
Year | 2010 |