You don't need or require a vent above a cooktop.
However having a vent above the cooktop or stove is a good idea to vent the cooking smells, smoke etc out of the kitchen and house.
The vent above a cooktop is a good idea to help improve the air quality of the house and get rid of pollutants from the cooking process in the home.
A range does not have to be vented and most codes do not make it a requirement to vent a range.
However venting a range with a range hood is a good idea as it helps get rid of smoke and cooking smells in your home and helps improve the air quality of your home and kitchen.
A range hood works by use of a fan that pulls the smoke and other smells out of the kitchen.
The fan creates a vacuum to suck the smells and smoke out of the air above the stove and send it outside.
A range hood is a device that mounts over the stove or range to help remove cooking smells and smoke from the kitchen as you cook on the range.
The range hoods job is to remove airborne grease, combustion products, fumes, smoke, heat, and steam from the air by evacuation of the air and filtration.
Although you can use a stove or range without a range hood the range hood is a good idea to keep your kitchen and homes air quality good.
A range hood keeps cooking exhaust, chemicals, and smoke out of your kitchen.
It improves your indoor air quality and streamlines your cooking experience.
Range hoods are made to improve the air quality of your kitchen after cooking.
They remove odors, grease, smoke, and fumes produced by using your stovetop.
The appliance sucks up the polluted air and filters it (as with a ductless model) or is carried to the exterior (with a ducted model).
Range hoods do not have to be vented to the outside.
But, ducted range hoods are almost always preferred over ductless hoods.
They remove all the smoke and cooking exhaust from your kitchen, while ductless hoods recirculate your cooking exhaust back into your kitchen.