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Mathematics 607: Basic Topology,   Fall
200\\
\centerline { Professor Frank Connolly, Room 235
CCMB }

\centerline{Text:  BASIC TOPOLOGY,   by M.A. Armstrong,
Springer Verlag(1983)  }




\centerline{MATERIAL TO BE COVERED}
Topological Spaces and Metric Spaces. Separation Properties.
The Tietze Extension Theorem. Compact Spaces, Product Spaces
and the Tychonoff Product Theorem.  Connectedness. Paths, Loops
and Homotopy. The Fundamental Group of a topological space.
Quotient spaces, topological groups, and orbit spaces.
Calculation of fundamental groups, and the classification of
Covering Spaces. Simplicial Complexes. The Euler Characteristic.

Smooth Manifolds, and Surfaces. Smooth Maps between
Manifolds. The Tangent Bundle of a
Smooth Manifold.


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