To determine which event occurred last, we need to consider the historical timelines associated with each of these events:
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The establishment of a trade network that connected the Swahili Coast with the Mediterranean, Persia, India, and China - This trade network began to develop around the late first millennium AD, particularly during the 9th century and intensified in the following centuries.
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The rise of independent sultanates on the Swahili Coast - The rise of these sultanates occurred from around the 10th century onward, particularly flourishing between the 11th and 15th centuries.
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The fall of the Axum Empire - The Axum Empire is generally considered to have declined around the 7th century AD, although its influence lingered for some time thereafter.
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The beginning of European colonialism in Africa - European colonialism in Africa began in earnest in the late 19th century, particularly after the Berlin Conference of 1884-1885, which formalized the scramble for Africa.
Based on this information, the event that occurred last would be the beginning of European colonialism in Africa.