If the oxidizer is oxygen from the surrounding air, the presence of a force of gravity, or of some comparable force caused by velocity, is necessary to produce convection, which removes combustion products and brings a supply of oxygen to the fire. Without gravity, a fire quickly surrounds itself with its own combustion products and non-oxidizing gases from the air, which exclude oxygen and extinguish the fire.
This does not apply if oxygen is provided to the fire by some process other than thermal convection. Fire can be extinguished by eliminating any among the aspects of the fire tetrahedron. Think about a natural gas flame, such as from a stove-top burner. Newsbreak topics on fire damage can be snuffed out by any of the following: turning off the gas supply, which removes the fuel source; covering the flame entirely, which smothers the flame as the combustion both utilizes the readily available oxidizer (the oxygen in the air) and displaces it from the location around the flame with CO2; application of water, which eliminates heat from the fire much faster than the fire can produce it (similarly, blowing hard on a flame will displace the heat of the currently burning gas from its fuel source, to the same end), or application of a retardant chemical such as Halon to the flame, which slows down the chemical reaction itself up until the rate of combustion is too slow to keep the chain response.
Methods to do this include balancing the input of fuel and oxidizer to stoichiometric proportions, increasing fuel and oxidizer input in this balanced mix, increasing the ambient temperature level so the fire's own heat is better able to sustain combustion, or supplying a catalyst, a non-reactant medium in which the fuel and oxidizer can quicker respond.
Left: Flame in the world; Right: Flame on the ISS A flame is a mix of reacting gases and solids producing visible, infrared, and sometimes ultraviolet light, the frequency spectrum of which depends on the chemical structure of the burning product and intermediate response items. In numerous cases, such as the burning of raw material, for example wood, or the incomplete combustion of gas, incandescent solid particles called soot produce the familiar red-orange glow of "fire".