Timeline for Does homeomorphism preserves the family of cones?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 11, 2012 at 20:30 | vote | accept | Evgeny | ||
| Jul 11, 2012 at 20:11 | answer | added | Lee Mosher | timeline score: 1 | |
| Jul 11, 2012 at 19:42 | history | edited | Evgeny | CC BY-SA 3.0 |
Corrected bad notation of objects
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| Jul 11, 2012 at 19:40 | comment | added | Evgeny | Sorry, but the last part of your construction seems to be vague for me. Is it possible that (in your example) image could be contained in a bigger cone? | |
| Jul 11, 2012 at 18:33 | comment | added | Lee Mosher | It is easy enough to construct a counterexample. $h$ will take the sphere of radius $1/3$ to itself, and will preserve the intersection of that sphere with the set $X_{C^*}$. Also, $h$ will take the sphere of radius $2/3$ to itself, but the $h$-image of the intersection of that sphere with the set $X_{C^*}$ will contain the intersection of that sphere with the complementary set $R^3 - X_{C^*}$. | |
| Jul 11, 2012 at 17:40 | comment | added | Evgeny | In context of my interest it is enough that $h$ maps cone into another cone, I even don't need $h(X_{C^*}) = h(X_{C'}) or $C^* = C'$. | |
| Jul 11, 2012 at 17:31 | comment | added | HorizonsMaths | I guess you meant $h(X_{C^*}) \subseteq X_{C^*}$! | |
| Jul 11, 2012 at 17:07 | history | edited | Evgeny | CC BY-SA 3.0 |
added 20 characters in body
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| Jul 11, 2012 at 17:05 | comment | added | Evgeny | That question appeared in my research, so I just wanted to check is this a common fact (that I've missed in my education) or should I cope with that question myself. | |
| Jul 11, 2012 at 17:00 | comment | added | Evgeny | Yes, I meant that. Sorry, I'll correct this moment | |
| Jul 11, 2012 at 16:59 | comment | added | Lee Mosher | Whether it does or not, though, this questions seems to me to be more suited to other sites such as math.stackexchange.com. It is not a research level question, which is what Math Overflow is for, as you will see if you read the faq. | |
| Jul 11, 2012 at 16:35 | comment | added | Lee Mosher | Does $Oz$ mean the $z$-axis intersected with the ball $B$? | |
| Jul 11, 2012 at 16:21 | history | asked | Evgeny | CC BY-SA 3.0 |