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 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.

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 covers the following
topics: Topological Spaces, Product and Quotient Spaces, Connected Topological
Spaces, Compact Topological Spaces, Countability and Separation Axioms.

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
Fundamental Group.

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 book explains the following topics:
Basic concepts, Constructing topologies, Connectedness, Separation axioms and
the Hausdorff property, Compactness and its relatives, Quotient spaces, Homotopy,
The fundamental group and some application, Covering spaces and Classification
of covering space.

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.

This note covers the following topics:Describing
Topological Spaces, Closed sets and Closure, Continuity and
Homeomorphism, Topological Properties, Convergence, Product Spaces
and Separation Axioms.