1 Algebraic sets, affine varieties, and the Zariski topology 4 1.1 Algebraic sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Hilbert basis theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Zariski topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.1 Proof that affine algebraic sets form closed sets on a t...

The recognition that within the area of computational geometry, the methods of algebraic topology can provide qualitative and shape information which isn't available from other methods. Algebraic topology provides a tool for visualization and feature identification in high dimensional data. Algebraic topology is an extremely useful framework for analyzing problems in distributed computing, such...

Noncommutative near-group fusion categories were completely classified in the previous work of first named author by using an operator algebraic method (and hence under assumption unitarity), and they shown to be group theoretical though corresponding pointed not identified. In this note we give a purely construction noncommutative starting from categorically Morita equivalent them.