"Science Stays True Here" Journal of Mathematics and Statistical Science, Volume 2016, 240-248 | Science Signpost Publishing Anti-Hausdorff I-Spaces Swapan Kumar Das Professor of Mathematics, University of Development Alternative (UODA), House No.- 80, Satmajid Road, Dhanmondi, Dhaka-1209, Bangladesh Email:swapanuoda@yahoo.com (corresponding author), +8801721830880 Subrata Majumdar Professor of Mathematics, University of Rajshahi, Rajshahi, Bangladesh Email:smajumdar2015@yahoo.com Nasima Akhter Professor of Mathematics, University of Rajshahi, Rajshahi, Bangladesh Email:nasima.math.ru@gmail.com Abstract This is the second paper on I-spaces. Here anti-Hausdorffness has been introduced for I-spaces and many topological theorems related to anti-Hausdorffness have been generalized to I-spaces, as an extension of study of infratopological spaces. Keywords: I-space, Trivial anti-Hausdorff I-space, Non-trivial anti-Hausdorff I-space, I-Continuous image, Quotient I-space, Irreducible spaces, Infratopological spaces. 1. Introduction In a previous paper [1] we have introduced I-spaces and studied some of their properties. In this paper we use the terminology of [1]. Some study of these spaces was done previously in ([2], [3], [4], [5]) in less general form. These spaces were called infratopological spaces. Anti-Hausdorff topological spaces and anti-Hausdorff U-spaces were introduced and studied in [6] and [7] respectively. In this paper the concept of anti-Hausdorff I-spaces have been introduced and a few important properties of such spaces have been studied. A number of interesting examples have been constructed to prove non- trivialness of such results.