Closed Curves and Topological Spaces

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Explores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Topology: Homotopy and Cone Attachments

Discusses homotopy and cone attachments in topology, emphasizing their significance in understanding connected components and fundamental groups.

Dimension Theory: Topological Space and Closed Subsets

Explores dimension theory in topological spaces and closed subsets, including height interpretation and additivity.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Green's Theorem in 2D: Applications

Explores the applications of Green's Theorem in 2D, emphasizing the importance of regular domains for successful integration.

Homotopy Extension Property

Introduces the homotopy extension property, exploring conditions for extending continuous maps.

Topology: Separation Criteria and Quotient Spaces

Discusses separation criteria and quotient spaces in topology, emphasizing their applications and theoretical foundations.

Topology: Classification of Surfaces and Fundamental Groups

Discusses the classification of surfaces and their fundamental groups using the Seifert-van Kampen theorem and polygonal presentations.

Functional Analysis I: Foundations and Applications

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