Reference no: EM13135293

Here is an example of what: 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 covers X.

Can you do something similar for the following spaces:

a) Reals with the "countable complement topology:" U open in X if X - U is countable or is all of X.

b) Reals with the "lower limit topology:" basis half-closed intervals [a,b)

c) Reals with the "upper limit topology:" basis half-closed intervals (a,b]

d) Reals with the "K-topology:" basis consists of open intervals (a,b) and sets of form (a,b) - K where K = {1, 1/2, 1/3, ... }