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:canterbury.ac.nz/oai:ir.canterbury.ac.nz:10092/2724 |
Date | January 2009 |
Creators | Hendtlass, Matthew Ralph John |
Publisher | University of Canterbury. Mathematics and Statistics |
Source Sets | University of Canterbury |
Language | English |
Detected Language | English |
Type | Electronic thesis or dissertation, Text |
Rights | Copyright Matthew Ralph John Hendtlass, http://library.canterbury.ac.nz/thesis/etheses_copyright.shtml |
Relation | NZCU |
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