Abstract We separate many of the basic fragments of classical logic which are used in reverse constructive mathematics. A group of related Kripke and topological models is used to show that various fragments of the Weak Law of the Excluded Middle, the Limited Principle of Omniscience, and Markov’s Principle, including Weak Markov’s Principle, do not imply each other.

Abstract This paper provides a Bishop-style constructive analysis of the contrapositive of the statement that a continuous homomorphism ofRonto a compact abelian group is periodic. It is shown that, subject to a weak locatedness hypothesis, ifGis a complete (metric) abelian group that is the range of a continuous isomorphism fromR, thenGis noncompact. A special case occurs whenGsatisfies 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.