View Proposal #298
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| ID | 298 |
|---|---|
| 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 |