A generalization of $ H $-closed spaces

Abstract

Whereas a space $ X $ can be embedded in a compact space if and only if it is Tychonoff, every space $ X $ can be embedded in an $H$-closed space(a generalization of compact space). In this paper, we further generalize, the concept of $H$-closedness into $ gH $-closedness and have shown that every connected space is either a $ gH $-closed space or can be embedded in a $ gH $-closed space. Also, in a locally connected regular space the concept of $ gH $-closedness is equivalent to the concepts of $ J $-ness and strong $ J $-ness due to E. Michael [7] and $ \theta $J-ness due to C.K. Basu et. al [1]. Several characterizations and properties of $ gH $-closed spaces with respect to subspaces, products and functional preservations (along with various examples) are given.