[opensuse 12.2 mantis] sed command -- how to

Greetings !!

I'm searching a way to delete all the spaces (0x20 '\ ' caracters) from a file named map3.cssm.

It works with sed 's/\ //g' map12x12/map3.cssm > map12x12/map003.cssm but I wanted to redirect the result displayed by sed to the file itself.

sed 's/\ //g' map12x12/map3.cssm > map12x12/map3.cssm resulted to an emply file
sed 's/\ //g' map12x12/map3.cssm >> map12x12/map3.cssm resulted to a double content !

How can I save the "seded" result to the file itself ?
And it there a way to apply this sed with a wildcard ?

sed 's/\ //g' map12x12/map*.cssm

Thanx in advance !!