International Journal of Pure and Applied Mathematics Volume 118 No. 4 2018, 883-894 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: 10.12732/ijpam.v118i4.5 P A ijpam.eu CHARACTERIZATIONS OF POINTWISE-I -CONTINUOUS, POINTWISE-I -OPEN AND POINTWISE-I -CLOSED MAPS Nitakshi Goyal 1 , Navpreet Singh Noorie 2 § 1,2 Department of Mathematics Punjabi University Patiala, 147002, INDIA Abstract: We obtain new characterizations of pointwise-I open (closed, continuous) maps with respect to an ideal I by using the concept of local function and # operator. We also generalize some known results. In addition various characterizations of pointwise-I -continuous onto maps in terms of saturated sets and pointwise-I -continuous injective maps are given. AMS Subject Classification: 54C08, 54C10 Key Words: Pointwise-I -Continuous, Pointwise-I -Closed and Pointwise - I -Open, Local Function, *-topology 1. Introduction In [7], Noorie and Bala used the sets of the form f # (E)= {y ∈ Y : f -1 (y) ⊆ E} to obtain new characterizations of open, closed or continuous mappings f : X → Y . On the other hand the study of properties of maps with respect to an ideal in topology is already a well researched topic in the literature. Starting with Kuratowski[6] and Vaidyanathaswamy[10], ideals in topological spaces have been used to study topological properties, where an ideal I on a topological space (X, τ ) is a collection of subsets of X which is closed under finite unions and closed downwards meaning that every subset of a member of I is in I i.e. if B ∈I then ℘(B) ⊆I , where ℘(B) means collection of all Received: April 24, 2017 Revised: November 29, 2017 Published: May 1, 2018 c  2018 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author