I-Lindelof spaces - Khalid Al-Zoubi; Bassam Al-Nashef (International Journal of Mathematics and Mathematical Sciences)
We define a space (X,T) to be I-Lindelof if every cover 𝒜 of X by regular closedsubsetsof the space (X,T) contains a countable subfamily 𝒜′ suchthat X=∪{int(A):A∈A′}. We provide several characterizations of I-Lindelofspaces and relate them to some other previously known classes of spaces, for example, rc-Lindelof, nearly Lindelof, and so forth. Our study here of I-Lindelofspaces also deals with operations on I-Lindelof spaces and, in its last part, investigates images and inverseimagesof I-Lindelofspacesundersome consideredtypesof functions.