A first course in topology

@inproceedings{Mccleary2006AFC,
  title={A first course in topology},
  author={John Henry Mccleary},
  year={2006}
}
A little set theory Metric and topological spaces Geometric notions Building new spaces from old Connectedness Compactness Homotopy and the fundamental group Computations and covering spaces The Jordan Curve Theorem Simplicial complexes Homology Bibliography Notation index Subject index. 
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  • M. Abu-Saleem
  • Mathematics
    Journal of Taibah University for Science
  • 2018
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References

SHOWING 1-10 OF 55 REFERENCES
Introduction to Topology
Topological spaces and operations with them Homotopy groups and homotopy equivalence Coverings Cell spaces ($CW$-complexes) Relative homotopy groups and the exact sequence of a pair Fiber bundles
Elements of algebraic topology
Elements of Algebraic Topology provides the most concrete approach to the subject. With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in
Algebraic Topology
The focus of this paper is a proof of the Nielsen-Schreier Theorem, stating that every subgroup of a free group is free, using tools from algebraic topology.
Fundamental Groups and Covering Spaces
This introductory textbook describes fundamental groups and their topological soul mates, the covering spaces. The author provides several illustrative examples that touch upon different areas of
Graphs, surfaces, and homology
Preface to the third edition Preface to the first edition List of notation Introduction 1. Graphs 2. Closed surfaces 3. Simplicial complexes 4. Homology groups 5. The question of invariance 6. Some
Knots and Links
Introduction Codimension one and other matters The fundamental group Three-dimensional PL geometry Seifert surfaces Finite cyclic coverings and the torsion invariants Infinite cyclic coverings and
Topology from the differentiable viewpoint
Preface1Smooth manifolds and smooth maps1Tangent spaces and derivatives2Regular values7The fundamental theorem of algebra82The theorem of Sard and Brown10Manifolds with boundary12The Brouwer fixed
Homology Theory: An Introduction to Algebraic Topology
This book is designed to be an introduction to some of the basic ideas in the field of algebraic topology. In particular, it is devoted to the foundations and applications of homology theory. The
A basic course in algebraic topology
1: Two-Dimensional Manifolds. 2: The Fundamental Group. 3: Free Groups and Free Products of Groups. 4: Seifert and Van Kampen Theorem on the Fundamental Group of the Union of Two Spaces.
From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes
1. Introduction 2. The alternating algebra 3. De Rham cohomology 4. Chain complexes and their cohomology 5. The Mayer-Vietoris sequence 6. Homotopy 7. Applications of De Rham cohomology 8. Smooth
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