**Core Concept**
The perivascular space, also known as the Virchow-Robin space, is a critical area in the brain where the blood-brain barrier (BBB) is breached, allowing for the exchange of substances between the blood and the brain parenchyma. This space is formed by the extension of the subarachnoid space around small penetrating arteries and veins.

**Why the Correct Answer is Right**
The correct answer is related to the anatomical relationship between the penetrating vessels and the surrounding brain tissue. The perivascular space is formed between the wall of small penetrating vessels and the pia mater, a delicate membrane that covers the surface of the brain and spinal cord. The pia mater is a key component of the BBB, and its extension around the penetrating vessels creates the perivascular space. This space is an important site for the clearance of waste products, including amyloid beta, from the brain.

**Why Each Wrong Option is Incorrect**
**Option A:** The arachnoid mater, a middle layer of the meninges, is not directly involved in forming the perivascular space.
**Option B:** The ependyma, a layer of cells lining the ventricles and central canal, is not related to the formation of the perivascular space around small penetrating vessels.
**Option C:** The subarachnoid space, while adjacent to the perivascular space, is not the structure between which the space is formed.

**Clinical Pearl / High-Yield Fact**
The perivascular space is a critical area for the clearance of amyloid beta, a key component of Alzheimer's disease pathology. Understanding the anatomy of this space is essential for developing effective treatments for neurodegenerative diseases.

**Correct Answer:** C. The pia mater.