Mildly generalized closed sets, almost normal and mildly normal spaces

The aim of this paper is to introduce and study the class of mildly generalized closed sets, which is properly placed between the classes of strongly generalized closed sets due to Sundaram and Pushpalatha in 2001 and weakly generalized closed sets due to Sundaram and Nagaveni in 1998. The relations with other notions directly or indirectly connected with generalized closed are investigated. Moreover we use it to obtain new characterizations and preservation theorems of almost normal spaces due to Singal and Arya and mildly normal spaces due to Singal and Singal, respectively.