This PDF covers the following
topics related to Topology : Topology of Metric Spaces, Topological Spaces,
Basis for a Topology, Topology Generated by a Basis, Infinitude of Prime
Numbers, Product Topology, Subspace Topology, Closed Sets, Hausdorff Spaces,
and Closure of a Set, Continuous Functions, A Theorem of Volterra Vito,
Homeomorphisms, Product, Box, and Uniform Topologies, Compact Spaces,
Quotient Topology, Connected and Path-connected Spaces, Compactness
Revisited, Countability Axioms, Separation Axioms, Tychonoff’s Theorem.
This PDF covers the following
topics related to Topology : Topology of Metric Spaces, Topological Spaces,
Basis for a Topology, Topology Generated by a Basis, Infinitude of Prime
Numbers, Product Topology, Subspace Topology, Closed Sets, Hausdorff Spaces,
and Closure of a Set, Continuous Functions, A Theorem of Volterra Vito,
Homeomorphisms, Product, Box, and Uniform Topologies, Compact Spaces,
Quotient Topology, Connected and Path-connected Spaces, Compactness
Revisited, Countability Axioms, Separation Axioms, Tychonoff’s Theorem.
This PDF covers the following
topics related to Topology : Preliminaries, Metric Spaces, Topological
Spaces, Constructing Topologies, Closed Sets and Limit Points, Continuous
Functions, Product and Metric Topologies, Connected Spaces, Compact Spaces,
Separation Axioms, Countability Properties, Regular and Normal Spaces.
String topology is the study of algebraic and
differential topological properties of spaces of paths and loops in manifolds.
Topics covered includes: Intersection theory in loop spaces, The cacti operad,
String topology as field theory, A Morse theoretic viewpoint, Brane topology.
Author(s): Ralph
L. Cohen and Alexander A. Voronov
This note covers the following
topics: Basic notions of point-set topology, Metric spaces: Completeness and its
applications, Convergence and continuity, New spaces from old, Stronger
separation axioms and their uses, Connectedness. Steps towards algebraic
topology, Paths in topological and metric spaces, Homotopy.
This note introduces
topology, covering topics fundamental to modern analysis and geometry. It also
deals with subjects like topological spaces and continuous functions, connectedness, compactness, separation axioms, and selected further topics such
as function spaces, metrization theorems, embedding theorems and the fundamental
group.
This note covers the following
topics: Topological Spaces, Product and Quotient Spaces, Connected Topological
Spaces, Compact Topological Spaces, Countability and Separation Axioms.
This note covers the following topics: Basic set theory, Products,
relations and functions, Cardinal numbers, The real number system, Metric and
topological spaces, Spaces with special properties, Function spaces,
Constructions on spaces, Spaces with additional properties, Topological groups,
Stereographic projection and inverse geometry.
This note will mainly be concered
with the study of topological spaces. Topics covered includes: Set theory and
logic, Topological spaces, Homeomorphisms and distinguishability, Connectedness,
Compactness and sequential compactness, Separation and countability axioms.
This note covers the following topics
: Background in set theory, Topology, Connected spaces, Compact spaces, Metric spaces, Normal
spaces, Algebraic topology and homotopy theory, Categories and paths, Path
lifting and covering spaces, Global topology: applications, Quotients, gluing
and simplicial complexes, Galois theory of covering spaces, Free groups and
graphs,Group presentations, amalgamation and gluing.
First part of this course note presents a rapid
overview of metric spaces to set the scene for the main topic of topological
spaces.Further it covers metric spaces, Continuity and open sets for
metric spaces, Closed sets for metric spaces, Topological spaces, Interior and
closure, More on topological structures, Hausdorff spaces and Compactness.