Lectures related to Partially ordered set

Relations and Sequences

Covers relations, sequences, and posets, emphasizing properties like anti-symmetry and transitivity, and introduces arithmetic and geometric progressions.

Integers: Elementary Concepts

Covers fundamental concepts related to integers, including properties of well-ordered sets and the principle of induction.

Möbius inversion: posets

Covers the Möbius inversion for posets, defining partially ordered sets and explaining the incidence algebra.

Partial Ordering: Relations, Sequences, Summation

Introduces partial orderings, lattices, and lexicographic orderings on Cartesian products.

Partial Ordering: Relations, Sequences, Summation

Explores partial orderings, divisibility relations, lattices, lexicographic ordering, comparability, and total orderings.

Equivalence Relations and Partial Orderings

Introduces equivalence relations, partitions, partial orderings, and total ordering concepts with examples and definitions.

Functional Analysis I: November 18, 2021

Covers partially ordered sets, maximal elements, upper bounds, and the Zorn lemma in functional analysis.

Relations and Sequences: Well-ordered Sets and Geometric Series

Explores equivalence relations, well-ordered sets, geometric series, and countable sets.

Lattices for Abstract Interpretation

Covers lattices, abstract interpretation, fixpoint analysis, Hoare logic, and partial orders with extreme elements.

Inverse Limits and Topologies

Explores inverse limits, profinite completions, and Hausdorff topologies in group theory and topology.