ON ^pA-CLOSED SETS IN DIGITAL PLANE
S. PIOUS MISSIER *
UGC Major Research Project-MRP-MATH-MAJOR-2013-30929, P.G. and Research Department of Mathematics, V.O. Chidambaram College, Thoothukudi 628 008, Tamil Nadu, India.
K. M. ARIFMOHAMMED *
UGC Major Research Project-MRP-MATH-MAJOR-2013-30929, P.G. and Research Department of Mathematics, V.O. Chidambaram College, Thoothukudi 628 008, Tamil Nadu, India.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we introduce the concept of ^pA-closed sets in topological space and characterize it using g#_o-kernel and _-closure. Moreover, we investigate the properties of ^pA-closed sets in digital plane. The family of all ^pA-open sets of (Z2; _2), forms an alternative topology of Z2. We prove that this plane (Z2; ^pAO) is T1/2 and T3/4. It is well known that the digital plane (Z2; _2) is not T1/2, even if (Z; _) is T1/2.
Keywords: Preopen sets, generalized closed sets, α-open sets, g# α-closed sets, ^pA-open sets, T1/2-spaces, T3/4-spaces, digital lines and digital planes