Lectures related to Compactly generated space

Covers extreme values of continuous functions on compact sets and differentiability.

Explores closure finiteness in CW complexes, proving compact subspaces are contained in finite subcomplexes through induction and characteristic maps.

Research Methods: Setting Up Experiments and Interview Guides

Explores setting up experiments, interview guides, and self-experimentation in research methods.

Topology: Compactness and Continuity

Explores compactness, continuity, and quotient spaces in topology, emphasizing the topology of lines in R² and the properties of compact sets.

Advanced Analysis II: Matrix Diagonalization

Covers matrix diagonalization, compact sets, continuity of functions, and the Mandelbrot set.

Differential Equations: Solutions and Periodicity

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Compact-open topology

Covers the compact-open topology, defining maps between spaces and discussing continuous maps and preimages in topology.

Stone-Weierstrass Theorem

Explores the Stone-Weierstrass theorem, proving uniform density of specific function families on compact sets.

Group Actions: Quotients and Homomorphisms

Discusses group actions, quotients, and homomorphisms, emphasizing practical implications for various groups and the construction of complex projective spaces.

Exponential Law: Mapping Spaces and Compactness

Explores the exponential law for mapping spaces and the role of compactness in topological theory.

Analyse II: Theorems on Continuous Functions and Extremums

Covers the theorems on continuous functions and extremums in compact sets.

Properties of Coatings

Covers the properties of coatings, including trivializing opens and automorphisms.

Advanced analysis II

Covers Jordan-measurable sets, Riemann-integrability, and function continuity on compact sets.

Advanced Analysis I: Continuous Functions on Compact Sets

Explores the necessity of uniform continuity for continuous functions on compact sets.

Preliminaries in Measure Theory

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Cauchy-Lipschitz Theorem

Explores the Cauchy-Lipschitz theorem for ODE solutions and linear transformations.

Lattices: Theory and Applications

Explores the theory of lattices, their properties, and applications in different mathematical contexts, emphasizing local-global principles.

Continuous Functions on Compact Sets

Explores continuous functions on compact sets, discussing boundedness and extremum values.

Bolzano-Weierstrass Theorem: Sequential Compactness in Hilbert Spaces

Explores the Bolzano-Weierstrass theorem in Hilbert spaces, showcasing sequential compactness and the construction of converging subsequences.

Quotients in Abelian Groups

Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.