Math 430 Definitions
topological space
topology
open set
discrete topology
trivial topology
finite complement topology
finer/coarser
basis (for a topology)
subbasis
lower limit topology on R
K topology on R
metric topology
product topology
subspace topology
closed set
closure and interior
limit point
T0,T1,T2(aka Hausdorff) (need to know only Hausdorff)
neighborhood
convergent sequence
continuous function
homeomorphism
topological property
quotient map
open map
closed map
quotient topology
saturated
topological group
separation
connected
totally disconnected
path
path connected
components (connected & path connected)
locally (path) connected
cover
subcover
compact
limit point compact
sequentially compact
locally compact
countable basis at x
first countable
second countable
dense
Lindelof
separable
Sorgenfrey plane
regular
normal
box topology (vs product topology)
topological group action
orbit
orbit space
END OF MIDTERM 1 MATERIAL
We also covered function spaces but I won't include these on the midterm.
Material for Midterm 2
homotopic, homotopy,
nullhomotopic, path homotopic,straightline homotopy
fundamental group (or first homotopy group)
-depends on base point
-continuous maps induce homomorphims of fund. gps.
simply connected
COVERING SPACES
evenly covered, covering map
fundamental group of circle (using covering spaces)
lifting correspondence
retraction, retract
brouwer fixed point theorem
deformation retract, deformation retraction
homotopy type, homotopy inverse, homotopy equivalence
using covering theory to get results about some fundametal groups like
torus, certain surfaces and wedge of circles
Free product of groups
Extension property
SEIFERT-VAN KAMPEN THEOREM
-using this to compute the fundamental group of a quotient of a polygonal
region.
I will not ask you about higher homotopy groups and you are not required
to know the details of CW complexes.