The first three volumes cover point set topology
, measure spaces, Hilbert and Banach spaces, distribution theory, the Fourier transform, and complex analysis.
Studying modules G over a ring R via their endomorphism ring EndR(G), the author discusses a wealth of results that classify G and EndR(G) via numerous properties, and uses results from point set topology
to provide a complete characterization of the direct sum decomposition properties of G.
It includes most of the basic results in manifold theory, as well as some key facts from point set topology
and Lie group theory.
Courses in complex function theory are often postponed in favor of courses in point set topology
and measure theory, they say, so they assume knowledge of these fields, along with calculus of several variables, epsilon-delta arguments, and Lebesgue's dominated and monotone convergence theorems.
It's a book that will work well with most math or computing science courses, on a subject that pertains to graph theory, point set topology
, elementary number theory, linear algebra, analysis, probability theory, geometry, group theory, and game theory, among many other topics.
Working from rigorous theorems and proofs, and offering a broad array of examples and applications he covers point set topology
, combinatorial topology, differential topology, geometric topology and algebraic topology in chapters on continuity, compactness and connectedness, manifolds and complexes, homotopy and the winding number, fundamental group, and homology.
Readers are assumed to be familiar with advanced calculus, point set topology
, linear algebra, and elementary group theory.