preface
parr i the line and the plane
chapter 1 what topology is about
topological equivalence
continuity and convergence
a few conventions
extra: topological diversions
exercises
chapter 2 axioms for r
extra: axiom systems
exercises
chapter 3 convergent sequences and continuity
subsequences
uniform continuity
the plane
extra: bolzano (1781-1848)
exercises
chapter 4 curves in the plane
curves
.homeomorphic sets
brouwer's theorem
extra: l.e.j. brouwer (1881-1966)
part ii mt. teac spaces
chapter 5 metrics
extra: camille jordan (1838-1922)
exercises
chapter 6 open and closed sets
subsets of a metric space
collections of sets
similar metrics
interior and closure
the empty set
extra: cantor (1845-1918)
exercises
chapter 7 completeness
extra: meager sets and the mazur game
exercises
chapter 8 uniform convergence
extra: spaces of continuous functions
exercises
chapter 9 sequential compactness
extra: the p-adic numbers
exercises
chapter 10 convergent nets
inadequacy of sequences
convergent nets
extra: knots
exercises
chapter 11 transition to topology
generalized convergence
topologies
extra: the emergence of the professional mathematician
exercises
part iii topological spaces
chapter 12 topological spaces
extra: map coloring
exercises
chapter 13 compactness and the hausdorff property
compact spaces
hausdorff spaces
extra: hausdorff and the measure problem
exercises
chapter 14 products and quotients
product spaces
quotient spaces
extra: surfaces
exercises
chapter 15 the hahn-tietze-tong-urysohn theorems
urysohn's lemma
interpolation and extension
extra: nonstandard mathematics
exercises
chapter 16 connectedness
connected spaces
the jordan theorem
extra: continuous deformation of curves
exercises
chapter 17 tychonoffs theorem
extra: the axiom of choice
exercises
parr iv postscript
chapter 18 a smorgasbord for further study
countability conditions
separation conditions
compactness conditions
compactifications
connectivity conditions
extra: dates from the history of general topology
exercises
chapter 19 countable sets
extra: the continuum hypothesis
a farewell to the reader
literature
index of symbols
index of terms
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