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.
L. Cohen and Alexander A. Voronov
This note explains the following topics:
Metric spaces, Topological spaces, Limit Points, Accumulation Points,
Continuity, Products, The Kuratowski Closure Operator, Dense Sets and Baire
Spaces, The Cantor Set and the Devil’s Staircase, The relative topology,
Connectedness, Pathwise connected spaces, The Hilbert curve, Compact spaces,
Compact sets in metric spaces, The Bolzano-Weierstrass property.
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 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 describes the
following topics: Set Theory and Logic, Topological Spaces and Continuous
Functions, Connectedness and Compactness, Countability and Separation Axioms,
The Tychonoff Theorem, Complete Metric Spaces and Function Spaces, The
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.
This is a collection
of topology notes compiled by Math topology students at the University of
Michigan in the Winter 2007 semester. Introductory topics of point-set and
algebraic topology are covered in a series of five chapters. Major topics
covered includes: Making New Spaces From Old, First Topological Invariants,
Surfaces, Homotopy and the Fundamental Group.
This is a set of lecture notes for a series
of introductory courses in topology for undergraduate students at the University
of Science, Vietnam National University–Ho Chi Minh City. Topics covered includes: Infinite sets,
Topological space, Generating topologies, Continuity, Subspace, Connectedness,
Separation, Convergence, Compact space, Product of spaces, Real functions and
Sp, Algebraic Topology, Differential Topology, Tangent spaces and derivatives,
Manifolds with boundaries.
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.