Modular Matrix Calculations in Finite Topological Spaces

Abstract

When crucial calculations are performed in a finite topological space(FTS), the matrix calculation method is more accurate and convenient than the traditional ways. However, even if the subset that is involvement in calculations is very small, all elements of the whole space are needed. This is a huge waste of time and space in applications. Therefore, we introduce the modular calculation method as a substantial improvement. Our notion is as follows: the topological space that are dealt with is partitioned into modules, and when a subset is involvement in calculations, only the relevant modules are considered rather than the whole space. Moreover, the subset is divided into smaller ones within relevant modules, thereby reducing the calculation range and ensuring the same results. Based on the modularization of the topological space, a module matrix calculation method is presented and investigated in detail. Finally, some examples are given to illustrate the modular calculation method.