Malaya Journal of Matematik, Vol.8, No.3, 1213-1218, 2020 https://doi.org/10.26637/MJM0803/0084 On almost contra δ gp-continuous functions in topological spaces J.B.Toranagatti Abstract The aim of this paper is to introduce a new class of almost contra continuity. The notion of almost contra δ gp-continuous functions is introduced and studied. Keywords δ gp-open set,δ gp-closed set,almost contra pre-continuous function,almost contra δ gp-continuous function. AMS Subject Classification 54C08,54C10. Department of Mathematics,Karnatak University’s Karnatak College, Dharwad-580 001, India. Corresponding author: jagadeeshbt2000@gmail.com Article History: Received 29 November 2019; Accepted 14 July 2020 c 2020 MJM. Contents 1 Introduction ...................................... 1213 2 Preliminaries ..................................... 1213 3 Almost contra δ gp-continuous functions ....... 1214 References ....................................... 1217 1. Introduction Recently, Baker(resp,Ekici,Balasubramanian and Laxmi) in- troduced and investigated the notions of almost contra conti- nuity [3] (resp, almost contra pre-continuity[10] and almost contra gpr-continuity [4] as a continuation of research done by Dontchev(resp,S.Jafari and T.Noiri and P.Jeyalakshmi) on the notion of contra continuity [9] (resp,contra pre-continuity [16] and contra gpr-continuity [18]. In this paper, we offer a stronger form of almost contra gpr- continuity called almost contra δ gp-continuity. Also,some properties and characterizations of the said type of functions are investigated. Throughout this paper, (U,τ ),(V,σ ) and (W,η )(or sim- ply U,V and W ) represent topological spaces on which no separation axioms are assumed unless explicitly stated and f:(U,τ )→(V,σ ) or simply f:U → V denotes a function f of a topological space U into a topological space V. Let M ⊆ U, then cl(M) = ∩{F: M ⊆ F and F c ∈ τ } is the closure of M. Also,int(M) = ∪{O: O ⊆ M and O ∈ τ } is the interior of M. The class of δ gp-open (resp, δ gp-closed, open, closed, regular open, regular closed, δ -preopen, δ -semiopen, e ∗ -open, pre- open, semiopen, β -open and clopen) sets of (U,τ ) is denoted by δ GPO(U) (resp,δ GPC(U), O(U), C(U), RO(U), RC(U), δ PO(U), δ SO(U), e ∗ O(U), PO(U), SO(U), β O(U) and CO(U)). 2. Preliminaries Definition 2.1. A set M ⊆ U is called δ -closed [36] if M = cl δ (M) where cl δ (M) = { p ∈ U :int(cl(G)) ∩ M = φ ,G ∈ τ and p ∈ G}. The complement of a δ -closed set is called δ -open Definition 2.2. A set M ⊆ U is called pre-closed [21] (resp, b-closed [1], regular-closed [33], semi-closed [19] and α - closed [22] if cl(int(M)) ⊆ M (resp, cl(int(M)) ∩ int(cl(M)) ⊆ M, M = cl(int(M)), int(cl(M)) ⊆ M and cl(int(cl(M))) ⊆ M). Definition 2.3. A set M ⊆ U is called δ -preclosed [27] (resp, e ∗ -closed [13], δ -semiclosed [26] and a-closed [14]) if cl(int δ (M)) ⊆ M (resp,int(cl(int δ (M)) ⊆ M, int(cl δ (M)) ⊆ M and cl(int(cl δ (M))) ⊆ M). Definition 2.4. A set M ⊆ U is called: (i) δ gp-closed [7] (resp, gpr-closed [15] and gp-closed [20]) if pcl(M) ⊆ G whenever M ⊆ G and G is δ -open (resp, regular open and open) in U. (ii) gδ s-closed [5] if scl(M) ⊆ G whenever M ⊆ G and G is δ -open in U Definition 2.5. A function f:(U,τ )→(V,σ ) is said to be: (i) almost contra continuous [3] (resp,contra R-map [11], δ - continuous [23], almost contra super-continuous [12], almost