A mosque in Harlem, at 2136 Eighth Avenue at 116th Street, is in danger of closing after its new landlord nearly doubled the rent, and is charging an extra fee if the mosque wants to use the empty second floor of the building. Landlord Homeside Development Corp. took over the mosque last year, and raised the rent from $4,000 to $7,500 per month. Mosque officials said they have to pay an additional $5,000 a month to use space upstairs, which remains empty. The landlord said the rent it is charging is fair because taxes on the building are $120,000 per year. However, according to the city Department of Finance, the landlord paid $38,702 in property taxes in 2008, and will likely pay $45,000 this year.