Final answer:
The papillary layer of the dermis contains the blood vessels and nerves closest to the surface of the skin, sitting just below the epidermis and above the thicker reticular layer and the hypodermis.
Step-by-step explanation:
The layer of the skin that contains the blood vessels and nerves that are closest to the surface of the skin is the papillary layer. The papillary layer is part of the dermis, which is the layer of skin directly under the epidermis. Within the dermis, the papillary layer contains numerous sensory receptors and blood vessels that provide nutrients to and remove wastes from dermal cells as well as cells in the lowest layer of the epidermis, the stratum basale. The dermis is a tough connective tissue that also includes the thicker reticular layer beneath the papillary layer. It's important to note that there are two main layers in the dermis: the papillary layer and the reticular layer, both containing blood vessels and sensory receptors.
Another relevant point is that the basement membrane lies between the dermis and the epidermis, serving as the boundary between these two skin layers. The dermis is also located above the subcutaneous tissue, or hypodermis, which is not the layer closest to the surface of the skin but rather provides support and nourishment to the dermis.