A separator for a lithium battery comprising: (a) a porous polymeric layer comprising a polyolefin, and (b) a nanoporous layer adjacent at least one of two opposing sides of said porous polymeric layer, said nanoporous layer comprising (i) inorganic oxide particles comprising boehmite particles and (ii) one or more polymer binders selected from cellulosic polymers, vinylpyrrolidone polymers and copolymers, polysaccharides, polyethylene oxides and polyvinyl alcohol that provide adhesive and cohesive strength to the nanoporous layer, wherein: a. any shrinkage of said separator at 200°C for 1 hour is less than 5%, wherein the shrinkage is measured by the change in the area of the separator after heating in an oven for 1 hour; b. said nanoporous layer comprises a total coating weight of 4.5 grams per square meter or less, wherein the coating weight is measured by the difference in weight of a 10 cm x 10 cm sample of the separator before and after coating the nanoporous layer on the porous layer, or before and after removing the nanoporous layer from the porous polymeric layer; c. the nanoporous layer comprises a solid portion and a volume fraction of said one or more polymer binders in the solid portion is between 15% and 50%, and d. said inorganic oxide particles have an average crystallite size between 5 nm and 90 nm, wherein the average crystallite size is measured by X-ray diffraction, or by a transmission electron microscope. (a) a porous polymeric layer comprising a polyolefin, and (b) a nanoporous layer adjacent at least one of two opposing sides of said porous polymeric layer, said nanoporous layer comprising (i) inorganic oxide particles comprising boehmite particles and (ii) one or more polymer binders selected from cellulosic polymers, vinylpyrrolidone polymers and copolymers, polysaccharides, polyethylene oxides and polyvinyl alcohol that provide adhesive and cohesive strength to the nanoporous layer, wherein: a. any shrinkage of said separator at 200°C for 1 hour is less than 5%, wherein the shrinkage is measured by the change in the area of the separator after heating in an oven for 1 hour; b. said nanoporous layer comprises a total coating weight of 4.5 grams per square meter or less, wherein the coating weight is measured by the difference in weight of a 10 cm x 10 cm sample of the separator before and after coating the nanoporous layer on the porous layer, or before and after removing the nanoporous layer from the porous polymeric layer; c. the nanoporous layer comprises a solid portion and a volume fraction of said one or more polymer binders in the solid portion is between 15% and 50%, and d. said inorganic oxide particles have an average crystallite size between 5 nm and 90 nm, wherein the average crystallite size is measured by X-ray diffraction, or by a transmission electron microscope. a. any shrinkage of said separator at 200°C for 1 hour is less than 5%, wherein the shrinkage is measured by the change in the area of the separator after heating in an oven for 1 hour; b. said nanoporous layer comprises a total coating weight of 4.5 grams per square meter or less, wherein the coating weight is measured by the difference in weight of a 10 cm x 10 cm sample of the separator before and after coating the nanoporous layer on the porous layer, or before and after removing the nanoporous layer from the porous polymeric layer; c. the nanoporous layer comprises a solid portion and a volume fraction of said one or more polymer binders in the solid portion is between 15% and 50%, and d. said inorganic oxide particles have an average crystallite size between 5 nm and 90 nm, wherein the average crystallite size is measured by X-ray diffraction, or by a transmission electron microscope.