JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology andâ€¦ (More)

If F is known to be free, with generators gi, /3 may be constructed by setting j3g; = &Â», with bi so chosen that pbi = agi. Conversely, let F have the cited property and represent F as a quotientâ€¦ (More)

The fundamental group iri of an arcwise connected topological space determines the one-dimensional homology groups of that space; indeed, the homology group Hi formed from finite chains with integralâ€¦ (More)

1. Introduction. Category, functor, and natural transformation of functors are notions of great generalityâ€”and consequent simplicity. They apply to many different parts of mathematics. Now 22 yearsâ€¦ (More)

The logical syntax of a symbolic language is a study of the formal properties of sentences of that language. It includes the formation rules which determine how the symbols of the language can beâ€¦ (More)