On the Structure of Topological Spaces

The structure of topological spaces is analysed here through the lenses fibrous preorders. Each space has an associated preorder and those preorders which return a are called spatial. A special class spatial consisting interconnected family indexed by unitary magma Cartesian studied here. Topological that obtained from preorders, with I, I-Cartesian characterized. characterization reveals hidden on such spaces. Several other characterizations obtained, attention drawn to case monoid equipped topology. wide range examples provided, as well general procedures obtain topologies data types groups their actions. Metric normed considered well.