I'm basically talking about the shirts that we usually wear to play sports like tennis and soccer
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It is a breathable sport t-shirt.
From Guide to breathability:
- Breathable garments do not ‘stop’ you sweating or producing moisture, which is a natural response, but allow drying to happen quickly. Breathability is particularly important in active wear. The more of your own body heat you will be using and producing, for example on an uphill trek, the more breathability you will need.
Sports Jersey or simply Jersey
a jersey as used in sport is a shirt worn by a member of a team, typically depicting the athlete's name and team number as well as the logotype of the team or corporate sponsor.
Depending upon the name of the sport/game, you may call these Football jerseys, Tennis jerseys, etc. Here are some jerseys on Google.