urban spaces and in other words urban design and architecture have been found with close linkage with art and beauty especially the arts such as painting and sculpture. addressing beauty at different areas such as creation of galleries to offer works of art, addressing form of urban spaces and representing works of art in urban environment have improved social life and increased identity, conse...

We prove Zilber’s Trichotomy Conjecture for strongly minimal expansions of 2-dimensional groups, definable in o-minimal structures:

avila and molina [1] introduced the notion of generalized weak structures which naturally generalize minimal structures, generalized topologies and weak structures and the structures α(g),π(g),σ(g) and β(g). this work is a further investigation of generalized weak structures due to avila and molina. further we introduce the structures ro(g) and rc(g) and study the properties of the structur...