Today I give you a mathematical pleasure, which you might want to take up and measure (What am I?)

Question

Today I give you a mathematical pleasure,

which you might want to take up and measure.

With a pole, or a hole, oh well,

you might want to read up on Borel.

My spirit can always be found in myself,

not somewhere else way up on a shelf.

With cups and caps you can bet,

that I'm nothing more than a well-equipped set.

Hint 1

No calculations, just math knowledge.

Hint 2

A hole or a pole is an allusion to topological spaces.

Hint 3

Let's just say that BSA, is not bovine serum albumin.

Rand al'Thor · Accepted Answer · 2020-04-25T16:16:36.240

4

You are, specifically,

the Borel $\sigma$-algebra on a topological space.

(Iterations of this answer:

I got immediately the general theme, but I put $\sigma$-algebra at first, then changed to topological space after the second hint was added, then finally put them together in the intended way after the third hint.)

Today I give you a mathematical pleasure,
which you might want to take up and measure.

Every topological space can be turned into a measurable space by using the Borel $\sigma$-algebra.

With a pole, or a hole, oh well,

Topology is about deformation of objects, but a hole cannot be deformed away.

you might want to read up on Borel.

Borel sets again.

My spirit can always be found in myself,
not somewhere else way up on a shelf.

A topology on a set contains the set itself as one of its elements, and so does a $\sigma$-algebra.

With cups and caps you can bet,
that I'm nothing more than a well-equipped set.

A topology is closed under certain kinds of union and intersection (cup and cap), and it's simply something that a set can be equipped with. Same for a $\sigma$-algebra.

edited Apr 25 '20 at 16:16

answered Apr 25 '20 at 05:55

Rand al'Thor

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You're so close! The thing you mention as the answer is not necessarily closed under intersection. I've added a hint. – Galen Apr 25 '20 at 14:42
1

@Galen OK, edited to a new answer. (I actually thought of this first - I know topology much better than measure theory - but then the mention of Borel sent me in the other direction.) – Rand al'Thor Apr 25 '20 at 16:06
You were half right the first time, now you're half right again. Put them together, and you'll be okay then. – Galen Apr 25 '20 at 16:09
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@Galen A topological measure space then? – Rand al'Thor Apr 25 '20 at 16:10
There's a name for it :P – Galen Apr 25 '20 at 16:11
I added a hint! – Galen Apr 25 '20 at 16:13
YUS! You got it! I am so gratified! Thank you for trying my riddle! – Galen Apr 25 '20 at 16:17
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@Galen Thank you for making a mathematical riddle! Btw, you might like this one (shameless plug). – Rand al'Thor Apr 25 '20 at 16:19

Today I give you a mathematical pleasure, which you might want to take up and measure (What am I?)

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