Research profile
Francis Su
Author of work recommended on this site.
- 10
- on the reading lists
Why people read this work
On the reading lists
What this site's guides and courses recommend by Francis Su, and why. Each opens its Library entry.
- A good place to startVideoLecture 1: Constructing the Rational Numbers
ℚ built from pairs of integers, the quotient construction this chapter uses.
Recommended in Guidebook 2A.3: Integers and Rationals
- VideoLecture 10: The Relationship Between Open and Closed Sets
Open and closed sets in a metric space and how they are related.
Recommended in Guidebook 2B.1: Metric Spaces
- VideoLecture 11: Compact Sets
Compactness by open covers, with examples of how it fails.
Recommended in Guidebook 2B.3: Compactness
- VideoLecture 13: Compactness and the Heine-Borel Theorem
The compact sets of ℝⁿ are the closed bounded ones.
Recommended in Guidebook 2B.3: Compactness
- VideoLecture 14: Connected Sets, Cantor Sets
Connected sets, the connected subsets of ℝ, and the Cantor set as a totally disconnected example.
Recommended in Guidebook 2B.4: Connectedness
- VideoLecture 17: Complete Spaces
Complete metric spaces and the role of Cauchy sequences.
Recommended in Guidebook 2B.2: Completeness and Contraction
- VideoLecture 2: Properties of Q
Order and field properties of ℚ, and the gaps that ℚ leaves.
Recommended in Guidebook 2A.3: Integers and Rationals
- VideoLecture 3: Construction of the Reals
Building ℝ out of ℚ, a construction to compare with the Cauchy-sequence one in this chapter.
Recommended in Guidebook 2A.4: The Real Numbers
- VideoLecture 6: Principle of Induction
Induction and well-ordering in an analysis course that builds the number systems first.
Recommended in Guidebook 2A.1: The Natural Numbers
- VideoLecture 7: Countable and Uncountable Sets
Countable and uncountable sets, in the course that ends with ordinals and transfinite induction.
Recommended in Guidebook 2A.8: Infinite Sets
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