Bol. Soc. Paran. Mat. (3s.) v. 30 2 (2012): 109–116. c SPM –ISSN-2175-1188 on line ISSN-00378712 in press SPM: www.spm.uem.br/bspm doi:10.5269/bspm.v30i2.14923 Note on contra δ ˆ g-continuous functions M.Lellis Thivagar and B.Meera Devi abstract: In this paper we introduce and investigate some classes of generalized functions called contra-δ ˆ g-continuous functions. We obtain several characterizations and some of their properties. Also we investigate its relationship with other types of functions. Finally we introduce two new spaces called δ ˆ g-Hausdorf spaces and δ ˆ g-normal spaces and obtain some new results. Key Words: δ ˆ g-closed, δ ˆ g-continuous,δ ˆ g-irresolute,δg-continuous. Contents 1 Introduction 109 2 Preliminaries 109 3 Contra-δ ˆ g-continuous 111 4 Applications 114 1. Introduction Ganster and Reilly [5] introduced and studied the notion of LC-continuous func- tions. Dontchev [3] presented a new notion of continuous function called contra- continuity. This notion is a stronger form of LC-continuity. Dontchev and Noiri [4] introduced a weaker form of contra-continuity called contra-semi-continuity. The purpose of this present paper is to define a new class of generalised continuous functions called contra-δ ˆ g-continuous functions and investigate their relationships to other functions. We further introduce and study two new spaces called δ ˆ g- Hausdorf spaces and δ ˆ g-normal spaces and obtain some new results. 2. Preliminaries Throughout this paper (X,τ ) and, (Y,σ)and (Z,η) represent non-empty topo- logical spaces on which no separation axioms are assumed unless or otherwise men- tioned. For a subset A of X, cl(A), int(A) and A c denote the closure of A, the interior of A and the complement of A respectively. Let us recall the following definitions, which are useful in the sequel. Definition 2.1. [12] The δ-interior of a subset A of X is the union of all regular open set of X contained in A and is denoted by int δ (A). The subset A is called δ-open if A = int δ (A), i.e. a set is δ-open if it is the union of regular open sets. 2000 Mathematics Subject Classification: 54A05, 54D10, 54C08 109 Typeset by B S P M style. c  Soc. Paran. de Mat.