On Matrix Representations of Homeomorphism Classes

Abstract

In this study, we investigate the matrix representations of homeomorphism classes. Considering well-known concepts such as the matrix of ones, column-sum, row-sum, one's complement, Hadamard product, and regular addition for matrices, we explore binary matrices' relationships with subsets of a finite set. The main results establish connections between matrix operations and set operations, providing insights into the structure of homeomorphism classes. The paper concludes with the formulation of a topology on a set based on specific matrix conditions.

Keywords

• Matrix representation
• Homeomorphism classes
• Topology.

References

1. Brualdi RA, Ryser HJ, et al. Combinatorial matrix theory, volume 39. Springer; 1991.
2. Eves HW. Elementary matrix theory. Courier Corporation; 1980.
3. Franklin JN. Matrix theory. Courier Corporation; 2012.
4. Ortega JM. Matrix theory: A second course. Springer Science & Business Media; 2013.
5. Stong RE. Finite topological spaces. Transactions of the American Mathematical Society. 1966;123(2):325–340.
6. Zhang F. Matrix theory: basic results and techniques. Springer Science & Business Media; 2011.