From topology to anti-reflexive topology

A topological space is a “space”, where “near” makes sense; it is formally defined by the Topological Neighborhood System (TNS). Here, we explore the concept of “conflict” by the system of “Anti-TNS”; by that we mean a “mathematical structure” that consists of a set of “punctured” neighborhoods, namely, the center point p of all neighborhoods of TNS has been removed. “Conflicts” are important concepts in computer security. The primary results is the axiomatization of ATNS. The main results are surprising: The set of the axioms is the same as that of topological spaces. Similar results for pretopological spaces also are obtained.