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8 Nov 2006: 4O:=<CKI@asgD6m{¡MO<>MK?b |7| IU6 J8;:U47L :@JMnMOD:@J¢{0:[ADIPM<=8;:ib |j b |g Sh,£?b | b |g SG[ADIPMub |7|; VT:iU6 J8;:U47L ... B64u<CKC º 1 jsgD6m{MO<>Mub |7|; U6 J8;:U47L :@I@G}<JDWWD:UMO:U47[tJD:nKMOIkCK[tKM@» t4O:=<ChJAD[aV :4ubvea¿>b b b d

27 Oct 2006: 0|f| a normed space? 3. Which of the following subsets of R2 are (a) open, (b) closed? ... Show that there exist disjoint closed subsets A, B of R (or R2 if you prefer) withd(A, B) = 0.

27 Feb 2006: ngi{_bie|g?t}&X;phYXXq&ZY[X+]. u:/u&9qfYucwE9& :q&>j uc Efc;A :q&> uc 9&E U ... k&mnbi]n}ZY[X}&XlZ<X;h<{y_]nbi]pZZ<ggi¥&Zb?_]b?]b?eoZYXhY]nb?ZY_iXµt:gphY{eb?ZY_gi]vg?tZY[_wWt9bpEZA[nb?Z«}&gfXWqZY[_wWh<X+}&

31 Jan 2006: O. é{ê_êcë¥ìë¢íî_ïðKñzò_óôìë¢íî_ôOO WZnWYXZY}YwXr|.qRqXERq}fYasd eYfvWYX> ][w >qWYXmO KKI|.0X}d efpcv ][w nKRaWhX}uowuqRqusoaZnÝ 4e|Yd ef_o{uY4Rx[w RqdQWs dexXr >XuRqvr_b.

10 Feb 2006: bWam%a_WØ y ¡Ø ¡Ø Ü: | >b[É]i_5] amWYWO>f;_C]i_W;>_hMàFá(â%âµBãäC9â>ã. ... Ì w Ã>kâYi[aeW_]i>] _>f;_¥ghVdh_b y | >bi]i>] _%_:ªib_]i_W_ÖeY_biXZ_ p VbiYiX];Vdc_:e phxzy Ì#!

4 May 2006: Prove that X+ is a topological space and prove that it is compact (N.B. ... 18. A continuous surjective map p : E B is a covering if every point b B has an openneighbourhood V such that the connected components of p1(V ) are open in

10 Mar 2006: O. ò«óXóôõôöXøùKúûXüýõôöXýOO v xw>)b]ef 6S [ikQW[þ v |Cÿrw |ÉÿN|ÿr9¿ÿrÉ)ÊCÿr)Ê|ÊÿN O ]>z |Cÿµ}9Ï¿ KQ)Q.

13 Nov 2006: ô-õ M £Æ¡= Ê 9¡ 9MòË 7µbKO-b f Û Úï!ÚÙ %>Û Rï i#Ml frx "%"%}l frx ri(! ... Õ-bpè Ð ZR0N? PO QC Þ¢Q> b# Øë Øì ÜÛ F Øì ëÍÚÙRÛ jì#ëÛcÚÜÉî(Ú#ïzì#ÛÑÜSRùÛë0% ñ Øí î=Ú RÙmì ëÛcÚÜ # Øë 4! «

22 Oct 2006: Then there exist a A, b B and c C with ab = c.In particular, this is true if all of A, B and C have size greater than 2n8/9. ... Equivalently, there exist a A and b B suchthat ab = c, as claimed.

26 Apr 2006: 49:904[þ%Hü;490HS68P?ý?üxú40hø684 F úLP?ý?þ%?ýý70þ:AYý76a=b[Rc;dfe , }r6n.E.32g4h4? ... þ6.04ø[ÉÈLÊ$[,ûB2iË([%b [%b ¿ dfe.