L0-projective topologies on linear spaces

On the Topologies of Spaces of Linear

Linear codes from projective spaces

The linear code Cs,t(n, q) of s-spaces and t-spaces in a projective space PG(n, q), q = ph, p prime, is defined as the vector space spanned over Fp by the rows of the incidence matrix of s-spaces and t-spaces. This code generalises the code of points and lines in a projective plane, which has been intensively studied since the 1970’s. In this paper, we give an overview of what is currently know...

On Generalized Injective Spaces in Generalized Topologies

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

Linear Spaces and Partitioning the Projective Plane

The aim of this paper is to settle a question about the partitioning of the projective plane by lines except for a small set. Suppose that Q is a set of points in the projective plane of order n and 6 is a set of lines that partitions the complement of Q. If Q has at most 2n&1 points and P has less than n+1+n lines, then these lines are concurrent. An example is given which shows that the condi...

Finite linear spaces and projective planes

In 1948, De Bruijn and Erdös proved that a finite linear space on v points has at least v lines, with equality occurring if and only if the space is either a near-pencil (all points but one collinear) or a projective plane . In this paper, we study finite linear spaces which are not near-pencils . We obtain a lower bound for the number of lines (as a function of the number of points) for such l...