Final answer:
The fascial system connecting core stabilization to breathing is known as deep fascia, with the transversus abdominis muscle as a specific example.
Step-by-step explanation:
The fascial system that connects core stabilization to breathing is known as the deep fascia. Deep fascia is a dense layer of connective tissue that surrounds individual muscles, groups of muscles, blood vessels, and nerves, binding those structures together in a fibrous membrane. It differs from the superficial fascia, which is primarily involved in connecting the skin to the underlying tissue. One specific example within the deep fascia is the transversus abdominis, which is the deep layer of the abdomen with fascicles arranged transversely around the abdomen. This muscle plays a key role in stabilizing the core and is indirectly involved in the breathing process, as a stable core supports the respiratory muscles.