Conversation so far:
Who did Michael Bloomberg run against in the 2001 election?
In the 2001 rescheduled primary, Bloomberg defeated Herman Badillo, a former Democrat Congressman, to become the Republican nominee.
Did Michael Bloomberg win the 2001 election?
Michael Bloomberg defeated opponent Mark J. Green in a close election held just weeks after the September 11 terrorist attacks.
How much did Michael Bloomberg spend on his campaign efforts in 2001?
Michael Bloomberg spent $73 million of his own money on his campaign, outspending Green five to one
Did Michael Bloomberg question the results of the 2001 election?
Was Michael Bloomberg originally the favorite in the race?
As Democrats outnumbered Republicans in NYC by a five-to-one margin in the city, it was widely believed that a Democrat would succeed Major Guiliani in City Hall

Question: Did Bloomberg announce plans to run in the next election?
Self-contained rewrite: Did Michael Bloomberg announce plans to run the next election after winning in 2001?