Definitions for arab world
(as a minimum) refers to Arabic-speaking independent states where Arabic is the main official and spoken language.
(as a maximum) refers to all states, territories and populations in North Africa, Western Asia and elsewhere where Arabic is a language of a significant minority or is a co-official language (including Israel, Eritrea, Djibouti, Somalia and South Sudan) or a territory is not recognised as independent, such as Palestine and Western Sahara.
U.S. National Library of Medicine
A historical and cultural entity dispersed across a wide geographical area under the administrative, intellectual, social, and cultural domination of the Arab empire. The Arab world, under the impetus of Islam, by the eighth century A.D., extended from Arabia in the Middle East to all of northern Africa, southern Spain, Sardinia, and Sicily. Close contact was maintained with Greek and Jewish culture. While the principal service of the Arabs to medicine was the preservation of Greek culture, the Arabs themselves were the originators of algebra, chemistry, geology, and many of the refinements of civilization. (From A. Castiglioni, A History of Medicine, 2d ed, p260; from F. H. Garrison, An Introduction to the History of Medicine, 4th ed, p126)