Topology (unitext)
by Marco Manetti /
2015 / English / PDF
4.1 MB Download
This is an introductory textbook on general and algebraic
topology, aimed at anyone with a basic knowledge of calculus and
linear algebra. It provides full proofs and includes many
examples and exercises.
This is an introductory textbook on general and algebraic
topology, aimed at anyone with a basic knowledge of calculus and
linear algebra. It provides full proofs and includes many
examples and exercises.
The covered topics include: set theory and cardinal
arithmetic; axiom of choice and Zorn's lemma; topological spaces
and continuous functions; connectedness and compactness;
Alexandrov compactification; quotient topologies; countability
and separation axioms; prebasis and Alexander's theorem; the
Tychonoff theorem and paracompactness; complete metric spaces and
function spaces; Baire spaces; homotopy of maps; the fundamental
group; the van Kampen theorem; covering spaces; Brouwer
and Borsuk's theorems; free groups and free product of
groups; and basic category theory. While it is very concrete
at the beginning, abstract concepts are gradually introduced. It
is suitable for anyone needing a basic, comprehensive
introduction to general and algebraic topology and its
applications.
The covered topics include: set theory and cardinal
arithmetic; axiom of choice and Zorn's lemma; topological spaces
and continuous functions; connectedness and compactness;
Alexandrov compactification; quotient topologies; countability
and separation axioms; prebasis and Alexander's theorem; the
Tychonoff theorem and paracompactness; complete metric spaces and
function spaces; Baire spaces; homotopy of maps; the fundamental
group; the van Kampen theorem; covering spaces; Brouwer
and Borsuk's theorems; free groups and free product of
groups; and basic category theory. While it is very concrete
at the beginning, abstract concepts are gradually introduced. It
is suitable for anyone needing a basic, comprehensive
introduction to general and algebraic topology and its
applications.
