Definitions of T_0, T_1, etc. Topological Spaces
A space S is T0 when for all x,y, (cl {x} = cl {y} ==> x = y)
A space S is T1 when for all x, /\{ U | x in open U } = {x}
A space S is Hausdorff when for all distinct x,y,
some open disjoint U,V with x in U, y in V
A space S is regular when for all x, open U nhood x
some open V with x in V, cl V subset U
A space S is normal when for all closed K, open U
K subset U ==> some open V with K subset V, cl V subset U
Exercise. Normal T1 ==> Regular T0 ==> Hausdorff ==> T1 ==> T0.
Exercise. Give an example of an irregular normal space.
Exercise. Demostrate that not only are T2, T3 and T4 not needed,
but also that their use is most confusing and misleading,
leaving one to be lost in some regular abnormal space.
Exercise. Don't ask about T_(1/2) and T_-1.
.
Relevant Pages
- Re: exercise
... work regular gym time into your life, as well as regular walks, running, sports - anything that gets you up and moving for some time every day. ... Diabetics on meds or insulin do need to take a little care about exercise timing, but you are not at that place yet. ... By the time soccer season arrived last year they were hurting more, I shouldn't have played soccer because after a few games I could barely walk. ... I am planing on going to the doc this year to get them fixed but for now the only exercise I can do without hurting them is my stationary bike, which is ok because I get to watch tv while I do it, I just need to get myself to do it. ...
(alt.support.diabetes) - Re: Exercise story
... I enjoy the gym mostly because I have met lot of people there, ... I used to go 5 or 6 days a week, regular as clockwork. ... I find it impossible to keep up any schedule of regular exercise which ... exercise and make a graph of how you're getting better or worse. ...
(alt.support.diabetes) - Re: back
... Gym is a no no for me. ... exercise makes your muscles stronger, and I think you recover more quickly ... I have found - having suffered from a worn spine since my mid twenties - ... that regular gentle exercise like swimming or walking medium distances ...
(uk.local.cumbria) - Re: Fat cyclists?
... I took my hat off to him, having come up the same hill a few ... like a normal human if he sticks to a regular regime. ... Healthy eating,combined with regular hardish exercise normally equals ... and cyclists with ...
(uk.rec.cycling) - Re: Fat cyclists?
... like a normal human if he sticks to a regular regime. ... Because it's a fact of life,overeating plus a lack of good ... Healthy eating,combined with regular hardish exercise normally equals ... So how do you explain thos epople who take no exercise and eat massive amounts of but never put on an ounce and those at the opposite end who take plenty of exercise, eat almost nothing but are still, according to your outlook) overweight? ...
(uk.rec.cycling) |
|
