Carrier frequency of a channel, bandwidth and modulation

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I don't understand the meaning of carrier frequency with respect to a transmission channel and the modulation phase with respect to the carrier frequency. I'm at a beginning level, so I try to explain what I get: "the carrier frequency of a channel is that frequency at which a channel works in the sense that the signals with that frequency are well transmitted by the channel". For example, Wi-Fi works either 2.4 GHz or 5 GHz carrier frequency.

The bandwidth of a channel is the set of frequencies a channel can transmit. But what is the meaning of bandwidth of a channel with respect its carrier frequency? If Wi-Fi works with a bandwidth of 10 MHz and it has a carrier frequency of 2.4 GHz means that all signals with frequency x where 2.4 Ghz - 5 MHz <= x <= 2.4Ghz + 5 MHz are well transmitted?

Instead, the modulation process is that process in charge of shifting/moving the input signal into the carrier frequency of the channel. Why do I need to use modulation? Because usually channels work with higher frequencies than frequencies of input signals and this is a suitable way to transmit information through a channel.

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Wi-Fi works either 2.4 GHz or 5 GHz carrier frequency [...]

Both 2.4 GHz and 5 GHz are just the freq. band names, and not the carrier frequencies themselves. Each band basically defines a set of channels, so there are 14 channels in 2.4 GHz, and much more in 5 GHz. Please see https://en.wikipedia.org/wiki/List_of_WLAN_channels.

If Wi-Fi works with a bandwidth of 10 MHz and it has a carrier frequency of 2.4 GHz > means that all signals with frequency x where 2.4 Ghz - 5 MHz <= x <= 2.4Ghz + 5 MHz > are well transmitted?

Each channel has its own carrier frequency (i.e. central frequency), e.g. channel 6 in 2.4 GHz corresponds to 2437 MHz. If the bandwidth (which can be configured) is 22 MHz, then the modulated signal on channel 6 will be in range from (2437 MHz - 11 MHz) to (2437 MHz + 11 MHz), i.e. from 2426 MHz to 2448 MHz.

As you can see, the range from 2426 MHz to 2448 MHz overlaps with other channels, and this is absolutely legal in Wi-Fi (unlike GSM).