Honam Mathematical J. 43 (2021), No. 1, pp. 123–129 https://doi.org/10.5831/HMJ.2021.43.1.123 CONNECTEDNESS IN IDEAL PROXIMITY SPACES Beenu Singh * and Davinder Singh Abstract. Two new concepts, namely, δ * -connectedness and δ * -component are introduced by using ideal in proximity spaces. A relation of δ * - connectedness with different types of connectedness that are considered in literature before is studied. It is shown that δ * -connectedness is a contractive property. 1. Introduction Kuratowski [6] and Vaidyanathaswamy [11] introduced the concept of ideal topological spaces. Subsequently, Ekici et al. [2, 3] defined the notion of con- nectedness in ideal topological spaces. Recently, various types of connectedness in ideal topological spaces are further investigated by Modak et al. [7]. Also, Hosny et al. [4] studied the notion of generalized proximity using ideal and proximity. The aim of this paper is to introduce the notion of δ * -connectedness by using ideal in proximity spaces that is analogous to the notion of ∗ s -connectedness in ideal topological spaces [2]. Also, we study δ * -component and the rela- tion of it with δ-component and ∗-component. In Section 2, we recall some basic definitions and results which will be used in further sections. We de- fine δ * -connectedness and examine the relationship between δ * -connectedness and different types of connectedness that are already in literature in Section 3. In the last section, we discuss the characterizations of δ * -connectedness and, examples are given for those characterizations that do not hold under this connectedness. Throughout this paper, by a proximity space (X, δ) (or X) [10], we mean a nonempty set X with an Efremoviˇ c proximity δ. Also, an ideal proximity space (X, δ, I ) will denote a proximity space (X, δ) with an ideal I in X. Further, a δ-closed (or δ * -closed) set in an ideal proximity space is a closed set with respect to the topology T δ generated by δ (or closed set with respect to T δ ∗ ). Received October 28, 2020. Revised December 22, 2020. Accepted January 5, 2021. 2020 Mathematics Subject Classification. 03E15, 54E05. Key words and phrases. δ-connected, δ-component, *s-connected, *-component, Ideal. *Corresponding author