With office and residential space in San Francisco and Silicon Valley becoming scarcer by the day, the East Bay city of Fremont, Calif., is girding for some spillover.

Last week, Lennar Corp. completed a deal to buy a 111-acre chunk of a former car-manufacturing plant in Fremont, 30 miles southeast of San Francisco, where it plans a dense mix of 2,200 apartments and houses, research-and-development space and offices, all centered around a new station for the commuter rail that leads to San Francisco.

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