This paper provides a Bishop-style constructive analysis of the contrapositive of the statement that a continuous homomorphism of R onto a compact abelian group is periodic. It is shown that, subject to a weak locatedness hypothesis, if G is a complete (metric) abelian group that is the range of a continuous isomorphism from R, then G is noncompact. A special case occurs when G satisfies a certain local path-connectedness condition at 0. A number of results about one-one and injective mappings are proved en route to the main theorem. A Brouwerian example shows that some of our results are the best possible in a constructive framework.
"Continuous isomorphisms from R onto a complete abelian group." J. Symbolic Logic 75 (3) 930 - 944, September 2010. https://doi.org/10.2178/jsl/1278682208