Air TV uses the Sling app, and it works through your local network Don't confuse your local network with your Internet connection. Those are not the same thing.
My Air TV device is connected to my network via Ethernet, not wireless. However, you can use the wireless connectivity if you prefer. My Air TV device, with the TV antenna cable attached, is located near my network router and switch, so I use an Ethernet cable to connect it. That is always the preferred way. However, if your antenna cable is not near your router, you can connect Air TV via WiFi, but again, wired is preferred.
By the way, none of the Air TV devices have HDMI, except for the Air TV Mini, which is actually a streaming device. You would have to switch your TV input to the HDMI for the Air TV Mini to watch it. The better devices, the Air TV 2 and the Air TV Anywhere, use your network to distribute the content to your Sling apps (Roku, or whatever platform).
Roku Community Streaming Expert
Note: I am not a Roku employee.
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