Many people are mistaken about betta. Other than the fact they have labyrinth organ which allow them to directly breath from the atmosphere, they are no different compare to any other tropical fish when it comes to the basic need.
The labyrinth organ only allow you to skip the air pump when it comes to equip your betta tank. You still need everything else which include ...
1. A proper sized fish tank (minimal 5 gallon is recommended for stable water temperature and chemistry)
2. An aquarium filter system
3. A heater
You must have all of the above or it is recommended not to get a fish.
Undersized tank really kill the fish. Since there is only so little water, any small change will result in the fluctuation in water temperature and water chemistry. Like all tropical fish, betta is fragile when it comes to unstable water conditions. It can stress or even kill them.
You will also have trouble to install proper equipments in undersized tanks. Betta is tropical fish, and they require 78~80F to stay healthy. Lower water temperature will lower their immune system and thus make it easy for them to get sick and die. Like all fish in aquariums, betta is not immune to ammonia poisoning which is produced by themselves as a waste. A filter system is mandatory or the fish will die pretty soon.
