We use the observed evolution of the galaxy cluster X-ray integral temperature distribution function between z = 0.05 and z = 0.32 in an attempt to constrain the value of the density parameter , \Omega _ { 0 } , for both open and spatially-flat universes .
We conclude that when all the most important sources of possible error , both in the observational data and in the theoretical modelling , are taken into account , an unambiguous determination of \Omega _ { 0 } is not feasible at present .
Nevertheless , we find that values of \Omega _ { 0 } around 0.75 are most favoured , with \Omega _ { 0 } < 0.3 excluded with at least 90 per cent confidence .
In particular , the \Omega _ { 0 } = 1 hypothesis is found to be still viable .