International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 43, Pages 2299-2305

I-Lindelof spaces

Khalid Al-Zoubi and Bassam Al-Nashef

Department of Mathematics, Faculty of Science, Yarmouk University, Irbid, Jordan

Received 15 July 2003

Copyright © 2004 Khalid Al-Zoubi and Bassam Al-Nashef. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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):AA}. 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.