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A firearm relies upon some kind of explosive powder to drive the slug out of the barrel.

My guess however is that in space (at GEO, or higher) a firearm would be unusable due to the extremes of temperature/pressure. Secondly the powder probably would not ignite when the hammer fell.

Are my assumptions correct? Can a firearm be used in space?

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Solid Rocket Boosters are powder-based firearms. – user10747 Jul 21 '12 at 20:18

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Consider the environment in which the propellent burns in a firearm. It is cramped space formerly packed tightly with stuff (the propellent, any necessary wadding and the bullet itself). There is damn little room for any atmosphere at all.

Where---especially in a cartridge system---do you think the oxidizer (NB: not necessarily oxygen!) is coming from anyway?

Most explosives do not run on atmospheric oxygen, then run on the oxidizer built in to the formulation. The only exceptions that I know of are fuel--air explosives and those are a specialized business.

You should expect cartridge firearms to work perfectly in space unless their parts vacuum weld. I'd be a little concerned about open-pan loose-power systems (do they initially burn environmental $\mathrm{O}_2$?, and in microgravity will they blow the power away before they initiate burning down the hole?), but I'd still take even odds that they work.

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What do 'open-pan', and 'loose-power' mean? – Everyone Jul 21 '12 at 17:56
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@Everyone: Some kinds of early firearms (matchlock, wheellock, flintlock) used an external ignition source which was applied to some loose-gun power sitting in a small tray (called a "pan") connected to the combustion chamber by a narrow hole. I've made some minor edits to expand on my concerns. – dmckee♦ Jul 21 '12 at 17:59
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@Everyone He is talking about weapons similar to the Brown Bess. See this video for more details. – mmc Jul 21 '12 at 18:00
Got it (+: In other words - the ammunition itself would probably work, but the design of the firearm itself might need to be modified to direct the expansion of gases, and possibly to reduce the risk of vacuum cementing/welding – Everyone Jul 21 '12 at 18:02
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@Everyone Apparently an automatic cannon installed in a soviet space station was test fired in the 70s. It's certainly feasible, but needs some care in the lubrication. – mmc Jul 21 '12 at 18:15

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