We give a Bishop-style constructive analysis of the statement that a continuous homomorphism from the real line onto a compact metric abelian group is periodic; constructive versions of this statement and its contrapositive are given. It is shown that the existence of a minimal period in general is not derivable, but the minimal period is derivable under a simple geometric condition when the group is contained in two dimensional Euclidean space. A number of results about one-one and injective mappings are proved en route to our main theorems. A few Brouwerian examples show that some of our results are the best possible in a constructive framework.
| Identifer | oai:union.ndltd.org:ADTP/274104 |
| Date | January 2009 |
| Creators | Hendtlass, Matthew Ralph John |
| Publisher | University of Canterbury. Mathematics and Statistics |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | Copyright Matthew Ralph John Hendtlass, http://library.canterbury.ac.nz/thesis/etheses_copyright.shtml |
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