View source for User:Alec

Hi, I'm Alec; I've done {{M|99.9\%}} of the work on this site easy and I am the administrator. You can contact me on my talk page (I use this site regularly) or at "alec" {{M|\mathcal{A}\top}} unified{{M|\rightarrow}}mathematics{{M|\cdot}} com 

The project has not gone entirely dormant. I've just been busy on other things [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 21:05, 8 May 2018 (UTC)

I must also remember to deal with pages tagged by [[Template:XXX]] as they have no grade/category system! Same for [[Template:Todo]] - I'm not sure how they're different!

: Don't forget about: [[:Category:Finished notes]]
: Or [[User:Alec/BookTemplate]]
: Or [[User:Alec/NewTodoTemplate]]
: Or [[Characteristic property of the disjoint union topology/Proof]]
: Or [[User:Alec/ParametricPages]]
: Or [[/Modules]]
: Or [[/Unnamed inequality]]
: Or [[/Exam Qs]]
: Or [[/Questions to do]]
: Or [[/Pages to do]]
: Or [[/Goals]]
: Or [[/Manifolds pages]]
: Or [[/Link templates]] added: [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 02:07, 31 December 2017 (UTC)
: Or [[/Template redirect test]] added [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 19:26, 31 December 2017 (UTC)
==[[User:Alec/Noticeboard|Noticeboard]]==
{{:User:Alec/Noticeboard}}
==[[User:Alec/Things not to forget|Things not to forget]]==
{{:User:Alec/Things not to forget}}
==[[User:Alec/Pages being worked on|Pages being worked on]]==
{{:User:Alec/Pages being worked on}}
==Notation==
{| class="wikitable" border="1"
|-
! Symbol
! Command
|-
! {{M|\trianglelefteq}}
| {{C|\trianglelefteq}}
|-
! {{M|\triangleq}}
| {{C|\triangleq}}
|-
! {{M|\ntrianglelefteq}}
| {{C|\ntrianglelefteq}}
|}
==Current projects==
Currently ensuring that all existing measure theory articles are "up to a decent standard" and working on Measure Theory, following Halmos' example (rings). 
* [[Notes:Halmos measure theory skeleton]] - notes for plan on definitions
* [[Site projects:Patrolling measure theory]] - "patrol" being the "decent standard" project.
* [[Site projects:Measure theory plan]] - implementation of plan.
* [[Site projects:Split set theory into elementary set theory]] - some things classified as "set theory" (like [[set subtraction]]) would be best classified as "elementary set theory". This project endeavorers to do that.
* [[Site projects:Patrolling topology]] - "patrol" being the "decent standard" project.

==Notes==
Diagram for [[Characteristic property of the product topology]]:
{| class="wikitable" border="1"
|-
|<center><span style="font-size:1.2em;"><m>\begin{xy}
\xymatrix{ 
 & & \prod_{\alpha\in I}X_\alpha \ar[dd] \\
 & & \\
 Y \ar[uurr]^f \ar[rr]+<-0.9ex,0.15ex>|(.875){\hole} & & X_b
\save
(15,13)+"3,3"*+{\ldots}="udots";
(8.125,6.5)+"3,3"*+{X_a}="x1";
(-8.125,-6.5)+"3,3"*+{X_c}="x3";
(-15,-13)+"3,3"*+{\ldots}="ldots";

\ar@{->} "x1"; "1,3";
\ar@{->}_(0.55){\pi_c,\ \pi_b,\ \pi_a} "x3"; "1,3";
\ar@{->}|(.873){\hole} "x1"+<-0.9ex,0.15ex>; "3,1";
\ar@{->}_{f_c,\ f_b,\ f_a} "x3"+<-0.9ex,0.3ex>; "3,1";
\restore

}


\end{xy}</m></span></center>
|-
! Diagram
|}
Characteristic property of the subspace topology:
* {{MM|1=\forall S\in\mathcal{P}(X)\left[\forall Y\forall\mathcal{K}\in\mathcal{P}(\mathcal{P}(Y))\left(\overbrace{\mathcal{T}(Y,\mathcal{K})\implies}^{\text{if }(Y,\mathcal{K})\text{ is a topology then} }\Big[\underbrace{\forall f\in\mathcal{P}(Y\times X)}_{\text{relations from }X\text{ to }Y}\big(\overbrace{\mathcal{F}(f)\implies}^{\begin{array}{c}\text{if }f\text{ is a}\\\text{function then} \end{array} }[\mathcal{C}(f)\iff\mathcal{C}(\iota_S\circ f)]\big)\Big]\right)\right]}}
==Things I want to use==
Linked list documentation diagram:
<syntaxhighlight lang="c">
            /*
             * B is the node to be removed.
             * We do this by binding A forward to C
             * 
             * BEFORE: 
             * ---> +---+---------> +---+---------> +---+-----
             *....  | A |           | B |           | C |    ....
             * -----+---+ <---------+---+ <---------+---+ <---
             * 
             * AFTER:       ,------------------.
             * ---> +---+--'        +---+-------'-> +---+-----
             *....  | A |           | B |           | C |    ....
             * -----+---+ <-.-------+---+        ,--+---+ <---
             *               `------------------'
             * 
             *  Note that B.previous.bindForwards(B.next) is the same
             *  as B.next.bindBackwards(B.previous)
             *  A nice side-effect of this is that provided one has a 
             *  ref counting scheme in place (which you need basically
             *  need for safe multi-threaded schemes anyway) any iterators
             *  "pointing" to B remain valid.
             *  Make sure that this "rail-road" situation where going
             *  forward and back MIGHT not be inverses is well documented
             *  and expected.
             */
</syntaxhighlight>