You are in the process of setting up a network infrastructure in Amazon Web Services $($AWS$)$ using Virtual Private Cloud $($VPC$)$ for your cloud$-$based application. During the network design phase, you encounter a crucial component that is responsible for establishing the connection between your network and the public internet. Your task is to identify and understand this specific component. Based on this scenario, answer the following question:

Question:

In the context of connecting your network to the public internet within an AWS Virtual Private Cloud $($VPC$),$ which component is used for establishing this connection?