Hey there, I don't know if anyone can help with this or not but what the heck.
Y=(1,5]. Which of the following subsets of Y are open and which are closed in Y, in the standard topology?
(0,1), (0,1], [1,2]
here's the context:
they were considering the subspace . The claim was, this subspace is not connected since we can express it as the union of two dis-joint, open sets, namely [0,1] and (2,3). Now instead of explaining to a dunce like me why [0,1] is open in the topology of X, the book simply warns, "remember, folks, we're dealing with a topology of X and not that of "
i tried looking back through the text to see what the author had said to make him believe this should not be a surprise to me...to no avail.
the best i could come up with is the definition, "Let be a topological space. The set is called closed when is open"
now i could not reconcile this with the claim [0,1] is open. is not , which is open, so should be closed?