(1) Place in order (0,0), (1,0), (0, 1), (1, 1). (2) Is (0, 1] x {0} an open set? (3) Is (0, 1] × {0} a closed set? (4) Is there any point in the order between (0, 1) and (1,0)? (5) Does this order have both a least and a greatest element? (6) What points of Y x X are limit points?
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Please solve 3.33 all the parts
![Problem 3.33. Let X =
{0,1} and Y = [0, 1] with their natural orders. Put the dictionary
order on Y x X. Put the order topology on Y × X. Answer the following:
(1) Place in order (0,0), (1,0), (0, 1), (1, 1).
(2) Is [0, 1] × {0} an open set?
(3) Is (0, 1] × {0} a closed set?
(4) Is there any point in the order between (0, 1) and (1,0)?
(5) Does this order have both a least and a greatest element?
(6) What points of Y x X are limit points?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53e9ab80-64ca-4d50-9be9-589e5309635d%2Fc0eb883a-0145-4235-901e-89f608833443%2F8x768yj_processed.jpeg&w=3840&q=75)
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