Can we say “being continuous with respect to the particular topology Kalai and Schmeidler chose, which is not obviously the correct topology to choose”? I would have chosen something like the quotient topology. The topology Kalai and Schmeidler chose is based on normalizations and, among other things, isolates the indifferent utility function (the one assigning the same value to all outcomes) from everything else.
Can we say “being continuous with respect to the particular topology Kalai and Schmeidler chose, which is not obviously the correct topology to choose”? I would have chosen something like the quotient topology. The topology Kalai and Schmeidler chose is based on normalizations and, among other things, isolates the indifferent utility function (the one assigning the same value to all outcomes) from everything else.
Agreed, that’s totally the wrong topology.