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general topology
(redirected from Point set topology)

   Also found in: Wikipedia 0.01 sec.
general topology [¦jen·rəl tə′päl·ə·jē]
(mathematics)
The branch of topology that studies the relationships between the basic topological properties that spaces may possess. Also known as point-set topology.


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It includes most of the basic results in manifold theory, as well as some key facts from point set topology and Lie group theory.
Additional topical coverage includes: * Sets and functions * Real numbers * Vector functions * Normed vector spaces * First- and higher-order derivatives * Diffeomorphisms and manifolds * Multiple integrals * Integration on manifolds * Stokes' theorem * Basic point set topology Numerous examples and exercises are provided in each chapter to reinforce new concepts and to illustrate how results can be applied to additional problems.
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.
 
 
 
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