By J. van Mill
The 1st a part of this e-book is a textual content for graduate classes in topology. In chapters 1 - five, a part of the elemental fabric of aircraft topology, combinatorial topology, measurement concept and ANR thought is gifted. For a pupil who will pass on in geometric or algebraic topology this fabric is a prerequisite for later paintings. bankruptcy 6 is an advent to infinite-dimensional topology; it makes use of for the main half geometric equipment, and will get to amazing effects quite speedy. the second one a part of this e-book, chapters 7 & eight, is a part of geometric topology and is intended for the extra complicated mathematician drawn to manifolds.
The textual content is self-contained for readers with a modest wisdom of normal topology and linear algebra; the mandatory heritage fabric is gathered in bankruptcy 1, or constructed as needed.
One can glance upon this booklet as a whole and self-contained evidence of Toruńczyk's Hilbert dice manifold characterization theorem: a compact ANR X is a manifold modeled at the Hilbert dice if and provided that X satisfies the disjoint-cells property. within the technique of proving this end result a number of fascinating and helpful detours are made.