Fuzzy Sets and Systems 147 (2004) 233–248 www.elsevier.com/locate/fss One-point compactications of ditopological texture spaces Murat Diker Department of Mathematics, Hacettepe University, Beytepe, Ankara 06532, Turkey Received 30 March 2001; received in revised form 22 May 2003; accepted 24 July 2003 Dedicated to the memory of Professor Do gan C  oker. Abstract In this paper a one-point compactication of a ditopological texture space is dened and a concept of local compactness introduced and shown to be additive in the class of ditopological texture spaces. An application to Hutton spaces is given. Here a compact extension of an Hutton space is obtained and a notion of local compactness is dened and shown to be productive in the class of L-topological spaces, where L is a Hutton algebra. c  2003 Elsevier B.V. All rights reserved. MSC: 54E55 Keywords: Texture space; Ditopology; Dicover bicompactness; Hutton algebra; L-topology; Locally dicover bicompactness; One-point dicover bicompactication 1. Introduction Texture spaces [1] provide an alternative setting for the study of L-fuzzy sets [12], fuzzy subsets, and generalized fuzzy subsets [14]. On the other hand the concept of ditopology generalizes certain lattice-theoretic aspects of topology, bitopology and xed-basis fuzzy topology. Material on textures and ditopologies, for instance in the areas of paracompactness, compactness and connectedness, may be found in the works of the author and Brown [2–4,10,11]. In this paper we construct a one-point compactication of a ditopological texture space, and introduce local compactness. We interpret these notions in the class of Hutton spaces [15,16]. In particular we obtain a compact extension for an L-topological space and dene an appropriate notion of local compactness in this setting, where L is a Hutton algebra [15,16]. First let us recall some basic denitions and results from [5–8]. E-mail address: mdiker@hacettepe.edu.tr (M. Diker). 0165-0114/$ - see front matter c  2003 Elsevier B.V. All rights reserved. doi:10.1016/S0165-0114(03)00325-7