I can only help you with supremum and infimum, maximum and minimum, boundary, and the classifications of open, closed etc.

I have no idea what "interior" or "closure" means, and i only have a very vague idea of what "accumilaation" means

a) [3,5)

Let S be the set [3,5)

supremum = 5

infimum = 3

maximum = doesnt exist

minimum = 3

boundary (explain): bounded above and below. Below by 3, since if s is an element of S, then 3<= s for all s in S. Above by 5, since if s is an element of S, 5>= s for all s in S

classification: Both open and closed. Closed at the lower bound, open at the upper bound

b) N --- natural numbers

supremum = doesnt exist (i guess you could say + infinity, dont hold me to this though)

infimum = 1

maximum = doesnt exist

minimum = 1

boundary (explain): Bounded below by 1. Since if n is an element of N, then 1<= n for all n in N. It is unbounded above

classification: closed at lower bound open at upper bound

c) { x is an element of Q: o <= x <= sqrt(2) } = Q and [0,sqrt(2)]

Let R be the set { x is an element of Q: o <= x <= sqrt(2) }

supremum = sqrt(2)

infimum = 0

maximum = doesnt exist

minimum = doesnt exist

boundary (explain): bounded below by 0, since if r is an element of R, 0 <= r for all r in R. bounded above by sqrt(2), since if r is an element of R, sqrt(2) >= r for all r in R

classification: open

I guess someone will come along soon who can help you with the other parts