spells – Do external, non-innate methods exist in Faerûn circa 1489 DR to situationally alter the efficacy of spellcasting?

Prior to D&D5e, Forgotten Realms lore included various situational methods and circumstances that could change the way spells and spellcasting worked. For example, the 1e product Volos’ Guide to All Things Magical includes a lengthy section on the use of various materials as special spell components. Using, say, a star sapphire in the casting of globe of invulnerability would increase level of spells warded off by the globe (see VGtATM p. 51). On the other hand, consuming the herb spellbane detailed in the 2e product Volo’s Guide to Cormyr would entirely suppress spellcasting ability for a period of time (VGtC p. 110).

Faerûn has changed a lot across editions, however, and nowhere is that more true than in the way magic and spells work. Maybe those old methods of amplifying or weakening spells and spellcasting are still effective, or maybe they aren’t. Is there any lore either way in 5e-era publications, i.e., in the Realms as they are post-Second Sundering, circa 1489 DR? Are there any other, different but comparable methods available?

To be clear, I’m interested here in methods that are temporary, ephemeral, and external to the caster and/or target — not innate abilities, learned skills, divine gifts, etc. Magic items are fair game, as are special substances (magical or otherwise). Even locations with special properties that change the way spells function would fit the bill.

Does this variant of discrete topology exist

The (usual) discrete topology on $X$ is defined here by letting every subset of $X$ be open (and hence also closed), and the discrete metric is defined by $ρ(x,y)=1: (x≠y)$ and $ρ(x,y)=0 :(x=y)$.

I think this clopen discrete topology is not good because if every set is both open and closed, then topological axioms should be changed so that it is (completely) different from the continuous topology. For example, in the continuous topology, open sets are closed under arbitrary union and finite intersection, and closed sets are closed under arbitrary intersection and finite union. However, in the clopen discrete topology, these should be changed to an axiom that any set is closed under arbitrary intersection and union. As a result, I propose a variant of discrete topology based on the Frechet filter on $ω$ that preserves open and closed sets separately as follows.

Definition 1: Let $mathscr{U}$ be a collection of subsets on $omega$. Then $mathscr{U}$ is a $ω$-topology if

  1. $varnothingnotinmathscr{U},:ωinmathscr{U}$.
  2. $mathscr{U}$ is closed under arbitrary union.
  3. $mathscr{U}$ is closed under finite intersection.

Definition 2: Let $mathscr{V}$ be a collection of subsets on $omega$. Then $mathscr{V}$ is a dual $ω$-topology if

  1. $varnothinginmathscr{V},:ωnotinmathscr{V}$.
  2. $mathscr{V}$ is closed under arbitrary intersection.
  3. $mathscr{V}$ is closed under finite union.

Definition 3: The open $ω$-topology $mathscr{T}$ is the Frechet filter on $ω$, i.e. $mathscr{T}={y⊂ωland ω-y:text{ is finite.}}$. The closed $ω$-topology $mathscr{T}^{c}=mathcal{P}(ω)-mathscr{T}$ is the dual of $mathscr{T}$. $mathscr{T}$ does not have a metric in general.

It is not hard to prove the following results.

Proposition 1:

  1. $varnothinginmathscr{T}^c,:ωinmathscr{T}$.
  2. $mathscr{T}$ is closed under arbitrary union and finite intersection.
  3. $mathscr{T}^c$ is closed under arbitrary intersection and finite union.
  4. $mathscr{T}$ is $T_0$.
  5. $mathscr{T}$ is compact.
  6. Each set in $mathscr{T}$ is infinite and each in $mathscr{T}^c$ is finite.
  7. Each finite von Neumann ordinal $n$ is a closed set in $mathscr{T}^c$.
  8. $ω$ is an accumulation point in $mathscr{T}$.
  9. $mathscr{T}$ is connected.

We can see that $mathscr{T}$ is better than the clopen discrete topology in that topological axioms (in definition 1.2 and 1.3) are preserved, while only $varnothinginmathscr{T}$ is not.
Also, we can prove the following lemma.

Lemma 2: $::O∈mathcal{H}iff(∃N∈ω)(∀n>N)(n∈O)$

One advantage of this $ω$-topology is that open sets are defined differently from closed sets. From lemma 2, we can also derive the $epsilon-N$ formula from the topological definition of continuity that $f$ is continuous iff $f^{-1}(O)$ is open for any open set $O$ in the same way as the $epsilon-delta$ formula is done.

My question is that is this discrete topology new or not.

shaders – Do alternatives exist for NVIDIA’s CG?

I recently finished writing the DirectX renderer for my game engine.
Now I have an OpenGL, DirectX as well as a not yet finished Vulkan renderer.

Well, the majority of the renderers work perfectly now but I have a problem: I need a shader programming language.

The problem is that OpenGL and Vulkan use GLSL but DirectX uses HLSL (and Apple’s Metal API uses MSL). So I searched for a High Level Shader Language and found only C for graphics from NVIDIA. But since this project was deprecated I looked for something else: Without success.

After several weeks of finding nothing, I decided to write my own language for it. But before I invest too much time I want to know if there are already existing alternatives for Cg.

set theory – In ZF, if injection from A to B doesn’t exist, then does surjection from A to B exist?

Claim : For non-empty sets $A, B$, (if there’s no injection from $A$ to $B$, then there exists a surjection from $A$ to $B$.)

I wonder how to prove or disprove that the 1st(2nd)-order logic sentence is generally true in ZF.

That claim is true in ZFC, since we can well-order both A and B, so A and B have cardinalities, the class of cardinalities are linearly ordered by inclusion. So, the claim isn’t generally false in ZF.

The converse is false in ZF, since both surjection and injection can exist between the same set A.
And the similar sentence : for non-empty sets A and B, (if there exists a surjection from A to B, then there exists injection from B to A.), is independent about ZF.

I guess the claim isn’t generally true in ZF, and I tried to deduce the sentence which is independent about ZF, but not yet succeeded.
Also, I couldn’t construct a model of ZF where the counter example exists.

How can I prove or disprove the claim is independent about ZF?

bogota – Do Water Chestnuts Exist in Colombia?

Do water chestnuts grow in Colombia? Or is it possible to buy them there? I’m assisting a film crew that’s on location for a cooking documentary, and they would like to blend an asian fusion dish with local Colombian ingredients. Unfortunately, they do not speak the local language and are having a hard time finding water chestnuts in Bogotá.

pnp powershell – update sharepoint list fields from exist sharepoint list

We need to fetch data from one SharePoint list and then update those fields data into another SharePoint list using pnp pwoershell command. Can anyone please guide or share pnp script for us. Thanks in advance.

Note: We are using SharePoint Online

postgresql – Select a row from one table, if it doesn’t exist, select from another table

How can I select a row from one table, but if it doesn’t exist, fall back to selecting it from a secondary table? Here’s a dumbed down version of what I’m trying to achieve

create table table_1 (
  person TEXT,
  favourite_number INT
  create table table_2 (
    person TEXT,
    favourite_number INT
  insert into table_1 (person, favourite_number) values 
  ('Bob', 1),
  ('Fred', 2)
    insert into table_2 (person, favourite_number) values 
  ('Bob', 30),
  ('Alice', 70)

I want to get the following result:

| person | favourite_number |
| Bob    | 1                |
| Alice  | 70               |
| Fred   | 2                |

Notice how it picks up Bob and Fred from the first table. Even though Bob appears in the second, because we’ve already got him we take him from the first table. Alice only appears in the second table.

This is what I’ve tried so far, but I can’t quite get all 3 returning back, please help.

from table_1 t1
where t1.person not in (select person from table_2)
from table_2 t2
where t2.person not in (select person from table_1)

online resources – How can I tell hotels exist that aren’t on the booking web sites?

First of all these websites, backed up by the GDSes as Stephen said, do not have a very good coverage of hotels (yet, it’s growing fast). There are still plenty of hotels to aggregate. And for hotels, getting aggregated usually means stricter conditions on their prices (little flexibility and high fee). And the main reason is that most hotels are not owned by large companies but individually owned.

So I would not expect, especially in a remote area, that you find all hotels on these sites. First you should extend your search to hostels (they have private rooms with private bathrooms), b&b, pensions, … sites like hostels.com or hostelworld.com allow to search for more than hostels. You can try airbnb, couchsurfing and the like.

I would try the tourism board as you did, but that works only if it is touristy. I would bet more on the directories. In most places of the world they are called yellow pages. And there you shall find a list. I can also think of contacting the ferry or airline company that brings you to the tiny island. On their website they might have a list of activities and accommodation. Give also a try to the guidebooks, they are usually done for that purpose. Maps like Google Maps or OpenStreetMap also display accommodation options, even though you should always double check they actually exist.

In the end, if hotels that have a website/can be booked online are still very expensive and you suspect some hotels are not online you can still show up there without a booking. If the area is not big you can cover it fast but if it is an island you should have a backup plan to be able to leave the area before the night not to be stuck there.

I remember getting to a Croatian island off-season and the hostel phone would not ring. I showed up and I could get a room for cheap, but I planned to take the ferry back if I could not find anything reasonable (and it was so dead I really was not sure it’d work). So yeah sometimes you can just give it a try.

How exactly do I use Lightning Network? Does it even actually exist?


Where is the download button for the official, highly trusted CLI application which works with Bitcoin Core? So that I can actually make Lightning transactions?

I’ve spent so long trying to figure out how to actually use this thing. I can’t have the current large fees for my products/services which are the same amount as the fee. That’s why I need to support Lightning Network. But how? Why is there no information?

interaction design – How do accessible forms work (what’s easier combobox or options) in whatever form factors they might exist in?

In addition to the keyboard, there are other devices used to enter data in a form, and I’m looking for the most efficient way to harness shortcuts familiar to these users.

What shortcuts for navigation, forms, or other might exist in standard and non default I/O for a computer device that accesses the internet? (voice nav mapping, etc)