Mathematics desk | ||
---|---|---|
< March 29 | << Feb | March | Apr >> | March 31 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Let F be an arbitrary closed subset of a topological space X. How can I find a real-valued continuous function f on X so that ? (I suppose we need to assume something on X.) -- Taku ( talk) 03:03, 30 March 2009 (UTC)
Thank you all for the answers; in particular, thank you PST for a nice example. I had a feeling that a partition of unity type argument (e.g., Urson's lemma) doesn't quite work. Also, thank you pma for putting a header. -- Taku ( talk) 21:58, 30 March 2009 (UTC)
Let X,d be a metric space with bounded distance, and consider the set of functions . It is the image of the Kuratowski-Wojdysławski embedding of X into Cb(X). But what is the closed convex hull of ? Does it contain every 1-Lipschitz function? Does it contain at least a constant function? Maybe under additional assumption on X? -- 79.51.237.63 ( talk) 19:14, 30 March 2009 (UTC)
I have memorized 126 decimal places of pi and I want to speed up my memorization. Is there any way to train my memory to work quicker and/or smoother with numbers? —Preceding unsigned comment added by Math321 ( talk • contribs) 19:54, 30 March 2009 (UTC)
I am trying to create a method to collect the rainwater from my roof to water my lawn. The tricky part is that most lawn watering methods would need 60psi through a standard 1" diameter hose to work properly. My question is that if I have a 500 gallon water tank elevated 12' off of the ground, how long will I have 60 psi through my 1" hose? How about for 30 psi? My hose will be connected at the bottom of the tank to improve the pressure. 65.121.141.34 ( talk) 20:37, 30 March 2009 (UTC)
Actually you would lose out a tiny bit if you consider the air pressure helping, because the atmospheric pressure is higher at lower elevations. —Preceding unsigned comment added by 65.121.141.34 ( talk) 20:16, 31 March 2009 (UTC)
Mathematics desk | ||
---|---|---|
< March 29 | << Feb | March | Apr >> | March 31 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Let F be an arbitrary closed subset of a topological space X. How can I find a real-valued continuous function f on X so that ? (I suppose we need to assume something on X.) -- Taku ( talk) 03:03, 30 March 2009 (UTC)
Thank you all for the answers; in particular, thank you PST for a nice example. I had a feeling that a partition of unity type argument (e.g., Urson's lemma) doesn't quite work. Also, thank you pma for putting a header. -- Taku ( talk) 21:58, 30 March 2009 (UTC)
Let X,d be a metric space with bounded distance, and consider the set of functions . It is the image of the Kuratowski-Wojdysławski embedding of X into Cb(X). But what is the closed convex hull of ? Does it contain every 1-Lipschitz function? Does it contain at least a constant function? Maybe under additional assumption on X? -- 79.51.237.63 ( talk) 19:14, 30 March 2009 (UTC)
I have memorized 126 decimal places of pi and I want to speed up my memorization. Is there any way to train my memory to work quicker and/or smoother with numbers? —Preceding unsigned comment added by Math321 ( talk • contribs) 19:54, 30 March 2009 (UTC)
I am trying to create a method to collect the rainwater from my roof to water my lawn. The tricky part is that most lawn watering methods would need 60psi through a standard 1" diameter hose to work properly. My question is that if I have a 500 gallon water tank elevated 12' off of the ground, how long will I have 60 psi through my 1" hose? How about for 30 psi? My hose will be connected at the bottom of the tank to improve the pressure. 65.121.141.34 ( talk) 20:37, 30 March 2009 (UTC)
Actually you would lose out a tiny bit if you consider the air pressure helping, because the atmospheric pressure is higher at lower elevations. —Preceding unsigned comment added by 65.121.141.34 ( talk) 20:16, 31 March 2009 (UTC)