Writing to file using Python

I have a file called output.txt, which I want to write into from a few functions around the code, some of which are recursive.
Problem is, every time I write I need to open the file again and again and then everything I wrote before is deleted.
I am quite sure there is a solution, didn't find it in all questions asked here before..

def CutTable(Table, index_to_cut, atts, previousSv, allOfPrevSv):
    print ('here we have:')

    print atts
    print index_to_cut
    print Table[2]
    tableColumn=0
    beenHere = False
    for key in atts:
        with open("output.txt", "w") as f:
            f.write(key)

and from another function:

def EntForAttribute(possibles,yesArr):
svs = dict()
for key in possibles:
    svs[key]=(yesArr[key]/possibles[key])
for key in possibles:
        with open("output.txt", "w") as f:
            f.write(key)

All output I have is the last one written in one of the functions..