A first course in topology

  title={A first course in topology},
  author={John Henry Mccleary},
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. 
Topological Classification of the Oriented Cycles of Linear Mappings
We consider oriented cycles of linear mappings over the fields of real and complex numbers. the problem of their classification to within the homeomorphisms of spaces is reduced to the problem of
A study of the conditions under which a topological space is metrizable, concluding with a proof of the Nagata Smirnov Metrization Theorem
Uniformization of Riemann surfaces revisited
We give a short, self-contained proof of the uniformization theorem for simply-connected Riemann surfaces.
Notes on Point Set Topology
The chapter provides a brief exposition of point set topology. In particular, it aims to make readers from the engineering community feel comfortable with the subject, especially with those topics
Trees as Level Sets for Pseudoharmonic Functions in the Plane
Let T be a finite or infinite tree and let V0 be the set of all vertices of T of valency 1. We propose a sufficient condition for the image of the imbedding ψ: T \V0 → $ {{\mathbb{R}}^2} $ to be a
Path connectedness, Compactness implies Continuity in a Path connected Complete Metric space
“A continuous function on metric space maps path connected set to path connected set and compact set to compact set.” This is a popular result in general metric space. In this article I prove the
Folding on manifolds and their fundamental group
  • M. Abu-Saleem
  • Mathematics
    Journal of Taibah University for Science
  • 2018
ABSTRACT In this paper, the induced sequence of folding and unfolding on the fundamental group will be obtained from a sequence of folding and unfolding on a manifold. The limit of folding and
A topological approach to divisibility of arithmetical functions and GCD matrices
Considering lower closed sets as closed sets on a preposet (P, ≤), we obtain an Alexandroff topology on P. Then order preserving functions are continuous functions. In this article we investigate
On the Topological Dynamics of Dynamical Manifolds and Their Fundamental Group
The paper aims to deduce the relation between the category of topology and algebra from viewpoint of geometry and dynamical system. We introduce and define a dynamical manifold as a manifold
Ideal boundaries of pseudo-Anosov flows and uniform convergence groups with connections and applications to large scale geometry
Given a general pseudo-Anosov flow in a closed three manifold, the orbit space of the lifted flow to the universal cover is homeomorphic to an open disk. We construct a natural compactification of


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