My problem is:(adsbygoogle = window.adsbygoogle || []).push({});

Consider an infinite set [itex]X[/itex] with thefinite complement topology. I want to show that any infinite subset [itex]A[/itex] of [itex]X[/itex] is dense in [itex]X[/itex].

Now, I can show that every point of [itex]X[/itex] is a limit point of [itex]A[/itex].

Can this help me in any way to show that [itex]A[/itex] is dense in [itex]X[/itex]. Or could someone provide me with an alternative method.

By the way, my understanding of dense is that a subset of a set is dense if its closure coincides with the set.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Infinite subset is dense

**Physics Forums | Science Articles, Homework Help, Discussion**