Course syllabus

Here is a rough schedule of the lectures. M refers to Munkres, GG to Gamelin/Greene.

Lecture 1       Cardinality of sets (M, Ch. 1, Section 7)

Lecture 2       Metric and Topological Spaces (M, Ch. 2.12, 2.13, 2.15, 2.16, 2.17, 2.20, 2.21 or GG, Ch. 1.1, 2.1, 2.2)

Lecture 3       Metric and Topological Spaces (M, Ch. 2.12, 2.13, 2.15, 2.16, 2.17, 2.20, 2.21 or GG, Ch. 1.1, 2.1, 2.2)

Lecture 4       Metric and Topological Spaces (M, Ch. 2.12, 2.13, 2.15, 2.16, 2.17, 2.20, 2.21 or GG, Ch. 1.1, 2.1, 2.2)

Lecture 5       Continuous Functions ( M. Ch. 2.18 or GG, Ch. 1.6, 2.3)

Lecture 6       Continuous Functions ( M. Ch. 2.18 or GG, Ch. 1.6, 2.3)

Lecture 7       Connectedness (M. Ch.3.23, 3.24 or GG, Ch. 2.8, 2.9)

Lecture 8       Compactness (M. Ch. 3.26 - 3.29 or GG, Ch. 1.5, 2.6)

Lecture 9       Compactness (M. Ch. 3.26 - 3.29 or GG, Ch. 1.5, 2.6)

Lecture 10     Completeness (M. Ch. 7.43, Ch.7.45-7.47 or GG, Ch.1.2, 1.8)

Lecture 11    Completeness (M. Ch. 7.43, Ch.7.45-7.47 or GG, Ch.1.2, 1.8)

Lecture 12     Completeness (M. Ch. 7.43, Ch.7.45-7.47 or GG, Ch.1.2, 1.8)

Lecture 13     Infinite Product Spaces and  Quotient Spaces ( M Ch. 2.19, 2.22 or GG Ch. 2.12, 2.13)