Annals of Fuzzy Mathematics and Informatics Volume 10, No. 6, (December 2015), pp. 883–894 ISSN: 2093–9310 (print version) ISSN: 2287–6235 (electronic version) http://www.afmi.or.kr @FMI c ⃝ Kyung Moon Sa Co. http://www.kyungmoon.com Urysohn’s lemma and Tietze’s extension theorem in soft topology Sankar Mondal, Moumita Chiney, S. K. Samanta Received 13 April 2015; Revised 21 May 2015; Accepted 11 June 2015 Abstract. The aim of this paper is to introduce a new type of soft mapping, continuous soft mapping and to establish Urysohn’s lemma and Tietze’s extension theorem in soft topological spaces using this type of continuous soft mappings. 2010 AMS Classification: 54A40, 03E72 Keywords: Soft topology, Soft open sets, Soft closed sets, Soft neighbourhood, Soft mapping,Ccontinuous soft mapping Soft normal space. Corresponding Author: S. K. Samanta (syamal 123@yahoo.co.in) 1. Introduction In 1999, Molodtsov [18] introduced the concept of soft sets, which is a new mathematical tool to deal with uncertainties. Soft set theory has rich potential for practical applications in different fields such as physical science, biological science, engineering, economics, social science, medical science etc. Maji et al. [15, 16] formulated some set theoretic operations on soft sets, and described an application of soft set theory to a decision making problem. Later on theoretical studies on soft sets have been done in different directions. To mention some of them, Aktas and Cagman [1] have introduced soft groups; Jun [11, 12] applied soft sets to the theory of BCK/BCI algebras and introduced the concept of soft BCK/BCI-algebras; Feng et al. [8] defined soft semi-rings; Shabir and Ali [25] studied soft semi-groups and soft ideals; Kharal and Ahmed [13] as well as Majumdar and Samanta [17] studied soft mappings etc. Shabir and Naz [26] came up with an idea of soft topological spaces. Afterward Zorlutuna et al. [28], Cagman et al. [3], Hussain and Ahmed [10], Hazra et al. [9], Aygunoglu et al. [2], Varol et al. [27], Sahin et al. [24] studied on soft topological spaces. In [6], Das & Samanta introduced a concept of soft metric. Recently investigations are going on in developing algebraico topological structures in soft setting [4, 7, 19, 20, 21]. In 2014, Mrudula Ravindran and Remya P. B. [22, 23] tried to extend Urysohn’s lemma and Tietze’s extention theorem in