did any anyone try to colonize this place?
Yes, Italy.
Libya
After the Italo-Turkish War (1911–1912), Italy simultaneously turned the three regions into colonies.
what was operation brevity? A limited offensive conducted in mid-May 1941. did it operate during any war? Second World War. who commanded the operation then? General Archibald Wavell where is he from? UNANSWERABLE who were the allied forces of the operation? 22nd Guards Brigade and elements of the 7th Armoured Division. where did this operation take place? Sollum–Capuzzo–Bardia. where is the  third place you mentioned located? Libya who were the first settlers in this place? Berbers
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Libya [SEP] Italian colonization (1911–1943)
After the Italo-Turkish War (1911–1912), Italy simultaneously turned the three regions into colonies. From 1912 to 1927, the territory of Libya was known as Italian North Africa. From 1927 to 1934, the territory was split into two colonies, Italian Cyrenaica and Italian Tripolitania, run by Italian governors. Some 150,000 Italians settled in Libya, constituting roughly 20% of the total population. Omar Mukhtar rose to prominence as a resistance leader against Italian colonization and became a national hero despite his capture and execution on 16 September 1931. His face is currently printed on the Libyan ten dinar note in memory and recognition of his patriotism.