Closure Spaces and Logic

This text examines closure spaces, an abstract mathematical theory, with special emphasis on results applicable to formal logic. The theory is developed, conceptually and methodologically, as part of topology. It shows how techniques and results from topology can be usefully employed in the theory of deductive systems, and that much of logical theory can be represented within closure space theory, the abstract theory of derivability and consequence can be considered a branch of applied topology. One upshot of this appears to be that the concepts of logic need not be overtly linguistic nor do logical systems need to have the syntax they are usually assumed to have. The text presupposes very little technical knowledge, but is more suited to someone with a background in symbolic logic or upper division or graduate mathematics. It should be of interest to logicians and computer scientists.