Open Access. Powered by Scholars. Published by Universities.®
Discrete Mathematics and Combinatorics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Discrete Mathematics and Combinatorics
Finite Matroidal Spaces And Matrological Spaces, Ziyad M. Hamad
Finite Matroidal Spaces And Matrological Spaces, Ziyad M. Hamad
Graduate Theses, Dissertations, and Problem Reports
The purpose of this thesis is to present new different spaces as attempts to generalize the concept of topological vector spaces. A topological vector space, a well-known concept in mathematics, is a vector space over a field \mathbb{F} with a topology that makes the addition and scalar multiplication operations of the vector space continuous functions. The field \mathbb{F} is usually \mathbb{R} or \mathbb{C} with their standard topologies. Since every vector space is a finitary matroid, we define two spaces called finite matroidal spaces and matrological spaces by replacing the linear structure of the topological vector space with a finitary matroidal …