TopologyDesigned as a text for a oneyear first course in topology, this authoritative volume offers an excellent general treatment of the main ideas of topology. It includes a large number and variety of topics from classical topology as well as newer areas of research activity. 
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LibraryThing Review
User Review  johnnylogic  LibraryThingDelightful text emphasizing pointset and the significance of limit sets. Much more readable than the elegant, yet rarified Kolmolgorov. Read full review
Contents
TOPOLOGICAL SPACES AND FUNCTIONS  1 
THE ELEMENTS OF POINTSET TOPOLOGY  37 
FURTHER TOPICS IN POINTSET TOPOLOGY  105 
THE ELEMENTS OF HOMOTOPY THEORY  149 
POLYTOPES AND TRIANGULATED SPACES  193 
SIMPLICIAL HOMOLOGY THEORY  218 
FURTHER DEVELOPMENTS IN ALGEBRAIC TOPOLOGY  282 
320  
365  
371  
Common terms and phrases
Axiom barycentric subdivision basis elements boundary Cantor set Cech homology chain groups chainmapping closed sets closed subset closure cochain coefficients cohomology collection compact Hausdorff space compact space component consider continuous mapping continuum coordinates COROLLARY covering Cp(L defined definition denote dimension equivalent Euclidean example EXERCISE finite number follows free group function geometric given groups CP(K Hausdorff space hence homeomorphism homology groups homology theory homotopy HP(K induced homomorphisms infinite integer intersection interval inverse limit isomorphic LEMMA lies limit point locally compact locally connected ncell nsimplex nsphere nonempty open set open set containing pchain pcycle pair Peano space polytope Proof prove reader real numbers result Section separable sequence simple chain simplex simplicial complex simplicial mapping subcomplex subgroup subspace Suppose Theorem topological group topological space topology triangulation union vector vertex vertices zero