Mr. Thompson's campaign strategy rests on winning large percentages of black and Latino voters.
Mr. Thompson, who is on his third marriage, mostly has remained quiet about his personal life.
WSJ: Politicians Get Personal in This Year's New York Mayoral Race
Mr. Thompson also suggested changes to the teacher evaluation system, making it less focused on tests.
None of those campaigns responded to requests for comment on Mr. Thompson's numbers Tuesday.
WSJ: Thompson Reports Uptick in Donations in New York City Mayor's Race
Mr. Thompson has been positioning himself as a more business-friendly Democrat than some of his competitors.
Mr. Bratton said his availability to speak about Mr. Thompson's public-safety plan wasn't an endorsement.
Mr. Thompson had a letter from his bishop explaining this to the Tax Court.
FORBES: Render Unto Caesar - Mormon Tithe Not A Necessary Expense In IRS Collection Case
But Mr. Thompson's candidacy was helped by his record running fast-growing PayPal, an acquaintance recalled.
By accusing Mr. Thompson of treating minorities unfairly, Ms. Quinn seemed to be directly targeting his base.
Mr. Thompson served as president of the now-defunct Board of Education before being elected comptroller in 2001.
Mr. Thompson said he had turned to other people besides Mr. Bratton for their views on crime.
Mr. Thompson also proposed higher pay for high-performing teachers who take on new responsibilities, like mentoring newer teachers.
Mr. Thompson didn't include specifics, such as how much money teachers would receive or how many would qualify.
Representatives for Mr. Thompson's main Democratic rivals either declined to comment or didn't respond to requests for comment.
Four other similar studios were built atop two other building along Tudor City Place, according to Mr. Thompson.
The proposal helps Mr. Thompson, a former city comptroller, differentiate himself on education policy from other Democratic mayoral candidates.
The announcement marks a significant increase in Mr. Thompson's fundraising pace, which has lagged behind his main Democratic rivals.
WSJ: Thompson Reports Uptick in Donations in New York City Mayor's Race
Mr. Thompson, who is black, came out against building the facility Thursday morning.
"We're quite pleased with that, obviously, " said Jonathan Prince, Mr. Thompson's chief strategist.
WSJ: Thompson Reports Uptick in Donations in New York City Mayor's Race
Mr. Thompson argued that the tithe was a necessary expense since it was required to hold his church offices.
FORBES: Render Unto Caesar - Mormon Tithe Not A Necessary Expense In IRS Collection Case
Mr. Thompson is a paid consultant for Lockheed Martin Corporation, which competes with SpaceX in various space ventures.
FORBES: SpaceX Responds To Forbes Contributor Loren Thompson
Mr. THOMPSON: I can see easily running a 100 gallon a day just through my two little tractors, easy.
Nothing is cluttered, nor does anything compete with Mr. Thompson, whose voice hasn't lost a bit of its quality.
WSJ: Still Electric After All These Years | Richard Thompson | By Jim Fusilli
Mr. Thompson's campaign sees the fundraising increase as part of a larger improvement in the candidate's position in recent weeks.
WSJ: Thompson Reports Uptick in Donations in New York City Mayor's Race
City Council Speaker Christine Quinn has been leading the field, while Public Advocate Bill de Blasio and Mr. Thompson trail her.
Dealing with Mr. Thompson would have been a conflict of interest for the search firm, which had helped eBay recruit him.
Mr. Thompson has been hovering around the middle of the pack in the crowded Democratic primary for mayor, according to recent polls.
Her closest rival was Mr. Thompson, whom she beat, 44% to 34%.
She didn't support Mr. Thompson when he challenged Mr. Bloomberg in 2009.
Mr. Thompson has a long history of attacking SpaceX in the press.
FORBES: SpaceX Responds To Forbes Contributor Loren Thompson
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