Lectures related to Metric spaces: topology

Introduces metric spaces, topology, and continuity, emphasizing the importance of open sets and the Hausdorff property.

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Advanced Analysis II: Recap and Open Sets

Covers a recap of Analysis I and delves into the concept of open sets in R^n, emphasizing their importance in mathematical analysis.

Boundary Analysis

Explores boundaries in sets, defining them as points not well separated from the set or its complement.

Norms and Convergence

Covers norms, convergence, sequences, and topology in Rn with examples and illustrations.

Open Balls and Topology in Euclidean Spaces

Covers open balls in Euclidean spaces, their properties, and their significance in topology.

Geometric Considerations in Rn

Covers the concept of intervals in Rn using geometric balls and defines open and closed sets, interior points, boundaries, closures, bounded domains, and compact sets.

Real Numbers: Absolute Value and Density

Covers absolute value, density of rationals, and real line topology.

Vector Spaces and Topology

Covers normed vector spaces, topology in R^n, and the principle of drawers as a demonstration method.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Euclidean Spaces: Properties and Concepts

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.

Norms and Distances in Analysis II

Discusses norms, distances, and the classification of open and closed sets in mathematical analysis.

Quotient Topology

Covers the concept of quotient spaces and the quotient topology, defining open sets and characterizing functions.

Delta-complexes: Structure and Maps

Covers the structure and uniqueness of maps in delta-complexes on top spaces.

Numerical Analysis and Optimization: Concepts of Distance and Subsets

Introduces key concepts in numerical analysis and optimization, focusing on distances, subsets, and their properties in R^n.

Vector Spaces and Topology

Covers vector spaces, topology, and proof methods like the pigeonhole principle in R^n.

Functional Analysis I: Foundations and Applications

Covers the foundations of modern analysis, introductory functional analysis, and applications in MAB111.

Distance, geodesics and complete manifolds: Complete manifolds

Explores distance, geodesics, and complete manifolds, emphasizing the existence of minimizing geodesics and the concept of metric completeness.

Properties of Convergence: Sequences and Topology

Discusses the properties of sequences, convergence, and their relationship with topology and compactness.