The invention provides a polymer, a polymer microfiber, a polymer nanofiber and applications including filter structure. Disclosed are improved polymeric materials, also disclosed are fine fiber materials that can be made from the improved polymeric materials in the form of microfiber and nanofiber structures. The microfiber and nanofiber structures can be used in a variety of useful applications including the formation of filter materials, polymer composition of addition or condensation polymers and aromatic resinous additives having a molecular weight of 500-3000 which are visible in the polymer and fiber layers. The condensation polymers are not the polymers of cyclic lactam and C6-10 diamine monomers or C6-10 diacid monomers. The diameter of the fiber is 0.01-5 micron, at least 30% of the fibers hold the line after exposed in the air of 140 DEG F and 100% humidity, and fibrous layers including the fibers.