Any territory detached from a city or district shall continue to be liable for the payment of principal, interest, and any other amounts which become due on account of any bonds, including revenue bonds, or other contracts or obligations of the district and any improvement district within which the detached territory has been situated, as are outstanding on the effective date of detachment. It shall be subject to the levying or fixing and collection of any of the following which may be necessary to provide for that payment:
(a) Taxes or assessments.
(b) Service charges, rentals, or rates.
(c) Both taxes or assessments and service charges, rentals, or rates.