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hw1-3.pdf
(from Basis for a Topology)
This shows how to determine which topologies contain which other topologies.
Closure of positive rational numbers - Can you give a brief reason why the closure of the positive rational numbers in each of the topologies below is the way it is indicated.
a) Reals with the "usual topology."
[0, inf)
b) Reals wit ...
Covers of topological spaces - Here is an example of what I would like you to try to do: In space Reals with the "usual topology.", call it X, the covering A={(-n, inf) | n natural number} of X contains no finite subcollection that ...
Topological spaces - Which of the following topological spaces is normal? Please give a proof why or why not. Thank you very much.
a) Reals with the "usual topology."
b) Reals with the "finite complement topology:" U ...
Topologies : Open Sets - • Let X:={a,b,c} be a set of three elements. A certain topology of X contains (among others) the sets {a}, {b}, and {c}. List all open sets in the topology T.
• Let X':={a,b,c,d,e} be a set of five e ...
Connected Topological Spaces - Please show why (briefly) each of the following top. spaces is or is not connected as indicated. Thank you.
a) Reals with the "usual topology." Why connected?
b) Reals with the "finite complement ...