Before Sept. 10:
- (2.1) infimum, supremum, triangle inequality, metric, Euclidean metric on Rn, discrete metric, ball centered at a of radius r, open subset of a metric space, closed subset of a metric space.
- (2.2) sequence converging to a point, Cauchy sequence, complete metric space, continuous function between metric spaces, homeomorphism, product metric
Before Sept. 17:
- (3.1, 3.2) topological space, topology, open set, indiscrete topology, discrete topology, metrizable topological space, closed set, interior point, accumulation point, boundary point, Hausdorff.
Before Oct. 1:
- (3.3, 4.1, 4.2) quotient map, quotient topology (you may use the defn. from class instead of the book), continuous function between topological spaces (you may use the defn. from the HW instead of the book), inclusion map, embedding, subspace topology, basis for a topology, local basis, first countable, second countable.
Before Oct. 8:
- (5.1, 4.3, 4.4) Product topology, identifying A and B along f, n-manifold, finite CW complex (this significantly simplifies the definition of CW-complex).
Before Oct. 1:
- (3.3, 4.1, 4.2) quotient map, quotient topology (you may use the defn. from class instead of the book), continuous function between topological spaces (you may use the defn. from the HW instead of the book), inclusion map, embedding, subspace topology, basis for a topology, local basis, first countable, second countable.
Before Oct. 22:
- connected, path connected, component.
Before Oct. 27:
- compact, sequentially compact
- concatenation of paths
- homotopy, basepoint-preserving homotopy of paths
- Fundamental group, including what the elements are, what the operation is, what the identity is, and what the inverse of an element is.