Methods of Applied Topology: Complexity of Data

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

Covers the concept of homeomorphisms in topology, focusing on functions that preserve topological properties.

Covers open and faded subspaces in topology with examples and exercises.

Covers the definition of edges, vertices, and cells in geometric shapes.

Covers data wrangling techniques using Hadoop, focusing on row versus column-oriented databases, popular storage formats, and HBase-Hive integration.

Delves into the transition from traditional to virtual museums, exploring digital archives and historical practices.

Explores the identification of the space SO(3) and the topology of SS-space of R₃(R).

Covers the digitization of vector objects in GIS, including creation, editing, and topology management.

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

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