8. Algebraic Topology
The sixth general mathematical framework is that of algebraic topology, which involves using the concepts and tools of abstract algebra to study topological spaces.
8.1 Betti numbers
Definition (Betti numbers). The k-th Betti number (k-dimensional Betti number) of a subset of A non-empty number is an integer denoted by βk (k = 0,.., n). In two dimensions: β0 is the number of connected components and β1 is the number of holes (i.e., cavities). In three dimensions: β0 is the number of connected components, β1 is the total number of holes, and β2 is the number of cavities (Figure
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Algebraic Topology
Dimension Theory I: Vector Dimension and Topological Dimension
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