bitcoin core – General information on the warning, when closing a wallet in pruned mode

A pruned knot will always catch up, what's the problem?

The problem comes from the opening of Bitcoin Core, but the wallet in question is not loaded in Bitcoin Core (because you have closed it). Bitcoin Core will continue to be synchronized and will receive new blocks and transactions. However, it will eliminate old blocks once it has stored the configured amount of block data.

For example, suppose your pruned node is synchronized with block 570000 and configured to hold 1,000 blocks of data. When you do Close the portfolio At block 570000, your wallet is synchronized with block 570000. But Bitcoin Core is still running and is receiving new blocks and transactions. 1000 blocks later, at block 571000, block 570000 is deleted. One block later, block 570001 is discarded.

Now, if you try to load your wallet again, he will try to catch up on the last block, so he's looking for block 570001 to start reanalysis. However, your node has already deleted the block and the new scan can not continue. In order for the 570001 block to scan it, you must download the complete blockchain again. This is what the warning serves.

During the entire period of closing your wallet, Bitcoin Core was still running. However, your wallet has not been loaded. As a result, he does not know how to analyze the transactions belonging to this portfolio. Even if he knew it, he would not know where to place the transactions he finds. So he's still catching up, but without the wallet in question, he can not find the deals that interest you.

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General topology – Proof: A set is closed if and only if it contains all its endpoints.

My complex analysis manual states the following:

A set is closed if its complement $ Omega ^ c = mathbb {C} – Omega $ is open. This property can be reformulated in terms of endpoints. A point $ z in mathbb {C} $ is said to be a limit point of the whole $ Omega $ if there is a sequence of points $ z_n in Omega $ such as $ z_n not = z $ and $ lim_ {n to infty} z_n = z $. The reader can now check that a set is closed if and only if it contains all its endpoints.

I want to prove the following:

A set is closed if and only if it contains all its endpoints.

Proof 1:

I start by assuming that the whole $ Omega $ contains all its endpoints.

$$ so Omega = {z in mathbb {C}: (z_n pas = z) cap ( lim_ {n to infty} z_n = z) }, $$

or $ z_n in Omega $ is a sequence of points.

And we have that

$$ begin {align} Omega ^ c & = {z in mathbb {C}: (z_n = z) cup ( lim_ {n to infty} z_n not = z) } & = {z in mathbb {C} } – {z in mathbb {C}: (z_n not = z) cap ( lim_ {n to infty} z_n = z) } \ & = mathbb {C} – Omega end {align} $$

Proof 2:

Assume that the whole $ Omega $ is closed.

So, $ Omega ^ c = mathbb {C} – Omega $ is open, since a set is closed if its complement $ Omega ^ c = mathbb {C} – Omega $ is open.

A set is open if each point of this set is an inner point.

Therefore, every point $ z in Omega ^ c $ is an interior point.

Therefore, every point of the set $ ( Omega ^ c) ^ c = Omega $ is not an interior point.

It's there that I'm not sure how to proceed. Given what the author has written, it is implied that he has provided all the necessary information for this evidence in the previous sections. However, I was unable to see how such proof can be made.

Before the textbook excerpt above, the author also gives descriptions of closed and open discs, as good as interior points as following:

The interior of $ Omega $ consists of all its interior points. Finally, a set $ Omega $ is open if every point of this set is an inner point of $ Omega $.

I've tried using this relationship between inner points and open sets, with the definition of closed sets above, to form a proof. However, I do not know if this is fruitful.

I would appreciate it a lot if people could take the time to review my work and help me with the proof 2.

General Hotel Supply Ideas

I tend to collect fridge magnets when I travel to a new place (usually for business). This is because they are small and easy to transport in the plane. I had used to pick up coffee cups and other items, but they were too big to be brought home and the woman ended up saying we had too many coffee mugs , anyway. So, the loving memories are for me. I find them easily in airports, but not so much in individual hotels (and I usually look.) I also prefer unusual magnets (hand-made, 3D, etc.) as opposed to a piece of soft plastic with an impression . For example, I bought a magnet in Georgia (in the United States) that contained a small container of the famous red clay from Georgia. I also bought in San Diego a magnet on which was glued a small seashell. In the Napa Valley, I bought a magnet with a small bottle of Chardonnay (obviously, it was plastic and filled with colored water but there was a fresh label on the bottle.) Obviously they all had professional art works, but they were cool because they had local materials. Note that these are all very small … maybe a square inch or more, on average.

Perhaps you could offer the hotel unique and handmade souvenir magnets that they would offer at gift shops. Even if they wear them now, if you have creative magnets made with local materials, this could be a hit for their customers.

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General topology – Chart commutativity in Top "Property similar to an elevator, but for covers"

Let $ psi, chi, phi $ to be continuous functions, with $ psi, xi $ onto. Is there necessarily a continuous function $ eta $ as the diagram flips up:
begin {tikzcd}
A arrow {d} { psi} arrow {r} { phi} & B arrow {d} { xi} \
C arrow {r}[dashed]{ eta} & D
end {tikzcd}

General Topology – Non-Limiting Marked Surfaces (Klein) with Limit

I'm trying to understand the topological classification of non-steerable surfaces with boundaries. It seems that the topological classification of closed surfaces without frontiers takes place as follows. According to the Wikipedia article, a closed area without limit can be topologically one of the following

  • It's a sphere;
  • This is a sphere with a number of handles $ h $;
  • It is a sphere with a number of crossed caps $ c $.

So my first question is this. The answer is probably NOT according to the theorem above!

  • First question: Is there not a closed surface with several handles $ h $ and a number of crosscaps $ c $?

According to this classification, and designating the number of Euler of a surface $ mathcal {R} $ by $ chi ( mathcal {R}) $, we can define the concept of gender $ g $ for an orientable or non-orientable surface as follows

  • For an orientable surface $ mathcal {R} $, we have $ g equiv frac {1} {2} (2- chi ( mathcal {R}) $. This coincides with $ h $, the number of handles;
  • For an orientable surface $ mathcal {R} $, we have $ g equiv 2- chi ( mathcal {R}) $. This corner with $ c $, the number of crosscaps;

However, I can imagine a non-steerable surface $ mathcal {R} $ with $ h $ manipulate, $ b $ limits $ c $ crosscaps, $ m $ points marked on the surface, and $ n_1, cdots, n_b $ points marked on the limit. Examples of such non-marked areas are given in Figures 12, 13, 14, 15 of this document. The first question is this

  • Second question: For such a surface $ mathcal {R} $ with handles, boundaries and crosscaps, are handles and crosscaps different concepts (as in the case of closed surfaces) or can they be considered in the same way? I mean, can a surface with a limit have handles and crosscaps at the same time?

  • Third question: Since $ mathcal {R} $ is non-orientable, remains the definition of gender $ g $ is given by $ g = 2- chi ( mathcal {R}) $?

Without delimited points, I think the number of Euler is given by

$$ chi ( mathcal {R}) = 2-2h-b-c-m. $$

  • Fourth question: What is the contribution of the delimited points $ n_1, cdots, n_b $ to the number of Euler of the surface?

With regard to these points,

  • Fifth question: How to topologically classify surfaces with $ h $ manipulate, $ b $ limits $ c $ crosscaps, $ m $ points marked on the surface, and $ n_1, cdots, n_b $ points scored on the limits?

I am also interested in building the compactification of surface space modules with $ h $ manipulate, $ b $ limits $ c $ crosscaps, $ m $ points marked on the surface, and $ n_1, cdots, n_b $ points marked on the limit.

  • Six question: Is there a good reference on the compactification of the space modulus of surfaces with $ h $ manipulate, $ b $ limits $ c $ crosscaps, $ m $ points marked on the surface, and $ n_1, cdots, n_b $ points scored on the limit?

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Transactions – What is the difference between mutual address financing and the general address starting with "1"?

I build raw transaction "0100000001b0e1a9cc83fbe8918a1cf20e0c72cf2fe3af252f228a3a0223943c2732f69bd8010000006b483045022100cf98600ba4f4d7bc748e36e4bb7eed48a26d7eab45bb813f65781ca7921a163702204f857a25574ba50c54373dc9fcdbba51ac1653b1007832b8314a7ccc2224d927012102534fd869124dff1cc99c430b97a5b6817b1f8343ce1e1de3ff71d4a3fc6c1592ffffffff02307500000000000017a9146cf00a2686081c15e931f7413b0f07561388c9c18764000000000000001976a914e093b1e8185d6b8136a80c8ab02e2f0bbfaf15c288ac00000000"

but it failed to broadcast on board, is there a difference between the financing of a multisig address and a normal address when creating a raw transaction and a transaction of signature?

You can also find the two types of addresses that appear in my exits. Does the Bitcoin network support this feature?