Surjective Identifications of Convex Noetherian Separations in Topological (C, R) Space

The interplay of symmetry algebraic structures in a space and the corresponding topological properties provides interesting insights. This paper proposes formation predicate evaluated P-separation subspace (C, R) space, where P-separations form countable finite number connected components. Noetherian P-separated subspaces within respective components admit triangulated planar convexes. vertices convexes are not interior open subspaces. However, points to locally dense surjectively identified another maintaining local homeomorphism. surjective identification two generates quasiloop–quasigroupoid hybrid variety. prime order allows cyclic group structure discrete set under bijection. containing admits linear translation operation, right-identity element preserves distribution other elements. Interestingly, convex oriented multiplicative structures. homeomorphic maintain path-connection, behaves as point separation. Surjectively admitting multiple preserve an alternative chained intersection property.