A lot of ideas from topology and analysis don't have obvious discrete analogues to me. At least, the obvious discrete analogues are vacuous.

• Compactness.
• Boundedness.
• Limits.
• The interior of a set.

I think a better question is which ideas have surprisingly interesting discrete analogues, like cohomology or scissors congruence.

A lot of ideas from topology and analysis don't have obvious discrete analogues to me. At least, the obvious discrete analogues are vacuous.

• Compactness.
• Boundedness.
• Limits.
• The interior of a set.

I think a better question is which ideas have surprisingly interesting discrete analogues, like cohomology or scissors congruence.