Jesse McKeown
May4-04, 10:34 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>So waaaaaaaaaaayy back in\nhttp://www.math.ucr.edu/home/baez/week149.html in the year we locally\ncall 2000, John Baez more or less asked for a nice description of what\nK(Z,3) looks like; and maybe one appears in later weeks, and maybe\nit\'s already been constructed here, but I\'m not quite sure how to go\nlooking for such a thing.\n\nAnd I also don\'t feel the least bit able to construct such a thing\nmyself, but I would like to ask what may be a relevant question, since\nK(Z,2) is identified as being (homotopic to) CP^\\infty, either as a\nforgotten flag of all finite-dimensional CP^n, or as the quotient\nspace of some Hilbert space H by the natural action of C^* on H. So\njust to be absolutely clear, I\'m curious as to which Hilbert space\nthis is; because, as we learned in Analysis last semester, there\'s a\ndistict H_\\kappa with complete ortho-normal system of cardinality\n\\kappa for all cardinals \\kappa, and that for \\kappa < \\lambda, there\nis no continuous surjection from H_\\kappa to H_\\lambda.\n\nI\'m willing to bet that the H in question is H_{\\aleph_0}, because\nCP^{\\aleph_0} is the space one gets with the above definition; and\nthis is maybe interesting because it looks like K(Z,2) is also the set\nof quantum states (\\aleph_0 of them forming a complete ortho-normal\nsystem) of a particle with no structure living in K(Z,1); I can\'t see\nyet why K(Z,1) should be considered the set of quantum states of a\nparticle living in Z = K(Z,0), but perhaps that\'s the wrong thing to\nthink about.\n\nAnyway, that\'s all!\n\n--Jesse\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>So waaaaaaaaaaayy back in
http://www.math.ucr.edu/home/baez/week149.html in the year we locally
call 2000, John Baez more or less asked for a nice description of what
K(Z,3) looks like; and maybe one appears in later weeks, and maybe
it's already been constructed here, but I'm not quite sure how to go
looking for such a thing.
And I also don't feel the least bit able to construct such a thing
myself, but I would like to ask what may be a relevant question, since
K(Z,2) is identified as being (homotopic to) CP^\infty, either as a
forgotten flag of all finite-dimensional CP^n, or as the quotient
space of some Hilbert space H by the natural action of C^* on H. So
just to be absolutely clear, I'm curious as to which Hilbert space
this is; because, as we learned in Analysis last semester, there's a
distict H_\kappa with complete ortho-normal system of cardinality
\kappa for all cardinals \kappa, and that for \kappa < \lambda, there
is no continuous surjection from H_\kappa to H_\lambda.
I'm willing to bet that the H in question is H_{\aleph_0}, because
CP^{\aleph_0} is the space one gets with the above definition; and
this is maybe interesting because it looks like K(Z,2) is also the set
of quantum states (\aleph_0 of them forming a complete ortho-normal
system) of a particle with no structure living in K(Z,1); I can't see
yet why K(Z,1) should be considered the set of quantum states of a
particle living in Z = K(Z,0), but perhaps that's the wrong thing to
think about.
Anyway, that's all!
--Jesse
http://www.math.ucr.edu/home/baez/week149.html in the year we locally
call 2000, John Baez more or less asked for a nice description of what
K(Z,3) looks like; and maybe one appears in later weeks, and maybe
it's already been constructed here, but I'm not quite sure how to go
looking for such a thing.
And I also don't feel the least bit able to construct such a thing
myself, but I would like to ask what may be a relevant question, since
K(Z,2) is identified as being (homotopic to) CP^\infty, either as a
forgotten flag of all finite-dimensional CP^n, or as the quotient
space of some Hilbert space H by the natural action of C^* on H. So
just to be absolutely clear, I'm curious as to which Hilbert space
this is; because, as we learned in Analysis last semester, there's a
distict H_\kappa with complete ortho-normal system of cardinality
\kappa for all cardinals \kappa, and that for \kappa < \lambda, there
is no continuous surjection from H_\kappa to H_\lambda.
I'm willing to bet that the H in question is H_{\aleph_0}, because
CP^{\aleph_0} is the space one gets with the above definition; and
this is maybe interesting because it looks like K(Z,2) is also the set
of quantum states (\aleph_0 of them forming a complete ortho-normal
system) of a particle with no structure living in K(Z,1); I can't see
yet why K(Z,1) should be considered the set of quantum states of a
particle living in Z = K(Z,0), but perhaps that's the wrong thing to
think about.
Anyway, that's all!
--Jesse