1. Consider the set X = {1, 2, 3, 4, 5}. Let X, ∅, {1, 3}, {1, 2},
{2, 3}, {1}, {2}, and {3} be the collection of all subsets of X
that are designated as open sets.
(a) Is X a topological space?
(b) Is it a topological space if {1, 2, 3} is added to the collection of open sets?
Explain.
(c) What are the closed sets (assuming {1, 2, 3} is included as an open set)?
(d) Are any subsets of X neither open nor closed?
1. Consider the set X = {1, 2, 3, 4, 5}. Let X, ∅, {1, 3}, {1, 2},
{2, 3}, {1}, {2}, and {3} be the collection of all subsets of X
that are designated as open sets.(a) Is X a topological space?
(b) Is it a topological space if {1, 2, 3} is added to the collection of open sets?
Explain.(c) What are the closed sets (assuming {1, 2, 3} is included as an open set)?
(d) Are any subsets of X neither open nor closed?
Euclid was a shallow fraud.
Actually, I think Euclid is a color, kind of between green and yellow with a hint of grey.
wow what is with all the tech stuff? Well no matter how you calculate it, the answer always comes up as vikking wins....:)
Thanks for holding for me, I've got it now!
Keep your filthy claws off my win!
Hole in one (my fifth).
Sixth hole -3
Total -17
So? I just lined up 18 balls, hit the first in line really hard and had and octadecimal-hole-in-one. They all landed in the right hole.
That makes me the winner.
Clean monkey paws? Have you seen what monkeys play with?
Diving in to steal TOZ's victory.
YAAR, ninjas be sneaky like that.
Winning the win thread for the win!
HUZZA, B!@*#ES!!!
oncest
Typo?
Anyway, I *won*. (See what O did there?)
victory!
Sieg!
YAAR, I be winnin'.