Victory at Crystal Palace maintained Liverpool's leadership ahead of the break.
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Van Dijk said, "Listen, I think there's always expectations towards different teams. Whatever the outside world thinks of us, we don't really care.
"We want to improve, we want to challenge, we want to compete until the final day and win and be successful. That's what we're focusing on – not what other expectations are. We've got a lot of points until now but we want to have a lot more.
"We know how tough the fixture list will be after the international break but why not enjoy it? I'm really looking forward to that and hopefully everyone involved with Liverpool as well."