The field of descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper we study the generalization where countable is replaced by uncountable. We explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in...

A generalized admissible triple is a triple T = (L, X,∆), where X is a set of size s + 1 ≥ 2, L is a Steiner system S(2, s + 1, st + 1), t ≥ 1, with point-set P and ∆ is a very nice map from P × P to the group Sym(X) of all permutations of the set X. Generalized admissible triples can be used to coordinatize generalized quadrangles with a regular spread and glued near hexagons. The idea of coor...

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...

the aim of this work is to describe the qualitative behavior of the solution set of a givensystem of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. in order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. this is done by the extension of ...