From topology to anti-reflexive topology

Author

Lin, Tsau Young ; Guilong Liu ; Chakraborty, Mihir K. ; Slezak, Dominik

Author_Institution

Dept. of Comput. Sci., San Jose State Univ., San Jose, CA, USA

fYear

2013

fDate

7-10 July 2013

Firstpage

1

Lastpage

7

Abstract

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.

Keywords

combinatorial mathematics; granular computing; rough set theory; security of data; topology; ATNS axiomatization; anti-TNS; antireflexive topology; big data applications; brute force combinatorial analysis; computer security; conflicts; granular computing; mathematical structure; pretopological spaces; punctured neighborhoods; rough sets; topological neighborhood system; topological space; Approximation methods; Computer security; Educational institutions; Information management; Rough sets; Topology; Anti-reflexive Topology; Granular Computing; Neighborhood Systems; Rough Sets;

fLanguage

English

Publisher

ieee

Conference_Titel

Fuzzy Systems (FUZZ), 2013 IEEE International Conference on

Conference_Location

Hyderabad

ISSN

1098-7584

Print_ISBN

978-1-4799-0020-6

Type

conf

DOI

10.1109/FUZZ-IEEE.2013.6622580

Filename

6622580