Open Extension Topology

Abstract

The paper contains the results which describe the properties of such general topological construction as open extension topology. In particular, we prove that this topology is not transitive. We find the base of the least cardinality for the topology and local one for the neighborhood system of every point. We calculate the interior, the closure, and the sets of isolated and limit points of any set. Also we prove that this space is path connected and is not metrizable, and investigate its cardinal invariants and separation axioms.