gn.general topology – Bottom half-continuity of a multivalued map $ F: X a 2 ^ Y $ in net terms

Leave $ X, Y $ Be two Hausdorff spaces and $ F: X to 2 ^ Y $ Be a multi-valued mapping We say that $ F $ is semicontinuous lower to $ x_0 in X $ yes for each $ y_0 in F (x_0) $ and any neighborhood $ U in mathcal N (y_0) $, there is a neighborhood $ V $ of $ x_0 $ such that
$$
F (x) cap U neq emptyset text {for all} x in V.
$$

In Aubin and Cellina. Differential inclusion, it is stated that the property is equivalent to

given any generalized sequence $ x_ mu a x_0 $ and any $ y_0 in F (x_0) $, there is a generalized sequence $ y_ mu in F (x_ mu) $ such that $ y_ mu a y_0 $.

I guess they meant net When they said generalized sequence.

I do not think this statement is trivial at all. In fact, I found proof of this from a different source that I think is not valid.

Leave $ (x_ mu) _ { mu in mathcal I} $ be a convergent network to $ x_0 $, the aforementioned test builds a network. $ y: D to Y $ of a directed set $ D subset mathcal I times mathcal N (y_0) $ defined by
$$
D: = {( mu, V): F (x_ mu) cap V neq emptyset }
$$

by choice
$$
y _ { mu, V} in F (x_ mu) cap V.
$$

It is not difficult to verify that $ (y _ { mu, V}) _ {(, V) a D} $ converges to $ y_0 $. However, your last step to find a map. $ sigma: mathcal I to D $ compose with $ and $ It seems invalid, since they leave $ sigma $ be an arbitrary section of $ pi: D to mathcal I $, where $ pi $ is the projection $ pi ( mu, V) = mu $.

However, I looked around and found an old paper from FrolΓ­k, On the topological convergence of sets., since 1960. It contains a statement that implies a weaker result (but it seems more reasonable) that could be summarized as follows.

Leave $ (M_ mu) _ { mu in mathcal I} $ be a network in $ 2 ^ Y $. So $ y_0 $ is in $ liminf M_ mu $ Yes and only if there is a network. $ pi: mathcal I & # 39; to mathcal I $ which residual in $ mathcal I $ and points $ y_ lambda in M ​​_ { pi ( lambda)} $ such that $ (y_ lambda) _ { lambda in mathcal I & # 39;} to y_0 $.

The test is almost identical to the previous one, but stopped by letting $ mathcal I & # 39; = D $, defined as in the previous test, and concluded the theorem without having to invoke a section $ sigma $ of $ pi $.

Question: Is the affirmation of Aubin and Cellina true? If so, where can I find a valid proof of that?

php: make custom publication type publications show up in regular publications on the site map (Yoast)

I have a custom publication type called Frequently Asked Questions, and I'm using Yoast SEO to generate a sitemap. The site map is generated as it should be, but creates a completely separate site map for the Frequently Asked publication type, so that example.com/faq-sitemap.xml. That makes sense, but I wonder if there is a way to keep the type of personalized Frequently Asked Publication, but that Frequently Asked publications appear below example.com/post-sitemap.xml instead, and then example.com/faq-sitemap.xml would not even exist anymore.

Here is the code to create the custom message type.

create_faq_post_type () {function
// Set user interface labels for the custom publication type
$ labels = array (
& # 39; name & # 39; => _x (& # 39; FAQs & # 39 ;, & # 39; General name of the publication type & # 39;),
& # 39; singular_name & # 39; => _x (& # 39; FAQs & # 39 ;, & # 39; Unique name of the publication type & # 39;),
& # 39; menu_name & # 39; => __ (& # 39; FAQs & # 39;),
& # 39; parent_item_colon & # 39; => __ (& # 39; Parent FAQs & # 39;),
& # 39; all_items & # 39; => __ (& # 39; All frequently asked questions & # 39;),
& # 39; view_item & # 39; => __ (& # 39; View FAQ & # 39;),
& # 39; add_new_item & # 39; => __ (& # 39; Add New FAQ & # 39;),
& # 39; add_new & # 39; => __ (& # 39; Add New & # 39;),
& # 39; edit_item & # 39; => __ (& # 39; Edit frequently asked questions & # 39;),
& # 39; update_item & # 39; => __ (& # 39; Update Frequently Asked Questions & # 39;),
& # 39; search_items & # 39; => __ (& # 39; Search Frequently Asked Questions & # 39;),
& # 39; not_found & # 39; => __ (& # 39; Not found & # 39;),
& # 39; not_found_in_trash & # 39; => __ (& # 39; Not found in Trash & # 39;)
);

// Set other options for the custom publication type
$ args = array (
& # 39; label & # 39; => __ (& # 39; faqs & # 39;),
& # 39; description & # 39; => __ (& # 39; frequently asked questions & # 39;),
& # 39; labels & # 39; => $ labels,
// Features that this CPT supports in Post Editor
& # 39; Support & # 39; => matrix (& # 39; title & # 39 ;, & # 39; editor & # 39 ;, & # 39; thumbnail & # 39 ;, & # 39; author & # 39 ;, & # 39; comments & # 39 ;, & # 39; Custom fields & # 39;),
& # 39; Hierarchical & # 39; => true,
& # 39; public & # 39; => true,
& # 39; show_ui & # 39; => true,
& # 39; show_in_menu & # 39; => true,
& # 39; show_in_nav_menus & # 39; => true,
& # 39; show_in_admin_bar & # 39; => true,
& # 39; menu_position & # 39; => 5,
& # 39; can_export & # 39; => true,
& # 39; has_archive & # 39; => true,
& # 39; exclude_from_search & # 39; exclude_from_search & # 39; => false,
& # 39; publicly_queryable & # 39; publicly_queryable & # 39; => true,
& # 39; taxonomies & # 39; => array (& # 39; category & # 39 ;, & # 39; post_tag & # 39;),
& # 39; rewrite & # 39; => array (& # 39; slug & # 39; => & # 39;% category% & # 39;)
);

// Faq record custom publication type
register_post_type (& # 39; faq & # 39 ;, $ args);
}

// Connecting the custom publication type function of frequently asked questions to the theme configuration
add_action (& # 39; init & # 39 ;, & # 39; create_faq_post_type & # 39 ;, 0);

A kind of strange request, but that's what SEO wants to do, unfortunately.

r – How to add an interactive heat map to a PDF?

I have created a map of heat in R and in heat. I need to add this heat map to a paper that I am publishing. The heat map is very large and the zoom of the heat source is very useful. Is it possible to add this heat map (it becomes an .html file when it is saved) in a PDF?
Is there a method to add an interactive heat map that is not a hyperlink?

: 2019 ri

: 2019 ri[IMG]https: //i106.fastpic*****big/2019/0605/59/d49a0771a1110c83e279a33337fe4659.jpg[/IMG] I : I : I : , Silentium I – .30. 2016: () :: ,,. – 68 000 000.6. . 2019, – .14: 40. 16:40. 19:00:, 13. 2019: .21. 2019 2. International GT Open. I. & # 39; (2019), .31 2019: (2019) .49. . . :,, Four. Five,. ,,, 1.-, (., -79-80., -The relationship in the context of international relations: problems and perspectives.6. 2019 Liberal Arts (2012) ,, 2018 – 2 () MP42 439 802 00 : 57 II: 3D: Men in Black: International., 01262019 – 23:13 2019 hd 1 + 1 International, 1 + 1 4: 4-6, 1. 1: 2, 100 2017 Transparency International & # 39; ,, – 30, 2019., 2018., .92.5%, 75.5%, 3.8%, 17.8%, 3.8%, 6.7%, Holtec International () 1,000 (!) 1 19:45 90.: ,, 1, 11:20, 13:40, 16:00, 18:20, 23:,! (76) ;, !!! 12. 2019. 1 () MP4 360p, -.,. 1 () 02:29: 2 () International Documentary Film Festival on Human Rights, & # 39; .67 DOCUSH DOCUMENT, Director: BIMCO (Bukovinian International Medical Congress). 40-49, .29. 2019 i 2019 hd kt 2: 11: 41.2019 2:.: Men in Black: Internationa l (2019)! (: 44) 2018 & # 39; (2018) & # 39 ;., ,,,. 2 (2002) HD.: (). 4 …: ,,,:.: Amblin Entertainment, MacDonald, Parks Productions.: "Men in Black – Protecting the Earth from the scum of the Universe". :.:, (1997) HD.: (). 4 .. 1. 2., The town: 11.:. : Men In Black: International. : . ,. ,. : : 13.:. : Men in Black International. . .2019: 42.: .2019 – .2019. : : : , -. , 02.. , 22 ,. ,. +38 (032) 297 50 05.:. , 9 ,. ,. : II: (30), 2 (30) ,: (6) ,: (13), 4 (20), -: (4), (18) ,: (1) 2: (2019). 5. 25 2019 .. 1 2019 (). I "23:10" "00:10" "02:00" "02:50" ". 05:50 06:00 11:35" "12:50" "14:00 4 17:15" "19: 00 19:30 20:00 20:30 21:00. 21:30 22:00 22:30 23:00 01:00 – 02:00 02:50 03:40. Data Map Data Map 2019 Final Report on the meaning of armed conflict in international law, 25, 75.:. You Tube. πŸ™‚ 1. πŸ™ 0. +1 1 .: – 2019 Avengers: End of game Trailer 2019 ::. & # 39;:. Release date: June 13, 2019. Original title: MEN IN BLACK: INTERNATIONAL Distributor: BH Film Distribution Company Release in 2D, 3D format Download DCP (1817.23 MB) Download HD 720p (Mb) Download HD 1080p (Mb). "-". 20:00. 5 201916: 42. "". 30 201815: 07. 1 (). BH Film Distribution Company .: Sony: MEN IN BLACK: INTERNATIONAL :: (8). :: (,), (:,), (:,:,), (,).:. (2019) By the 2018-12-21 In Video .: Men in B international shortcoming, 2019, – 2015. by the 2015-01-17 in Video. () "" – 90-, & # 39; 1 (2017). By Zala Zosi on 2017-06-09 in Video 30. Google Street View,,. & # 39; – ,,. & # 39; () ,,. : – 1997 ,. ,,,,. 05/20/2019 19:45. The CW ,,. – BBC , 36. -. . : 0 .. 3 3 (2012). : : 1460. 2019 ,. ,. 2019 :. .2019. 22. & # 39; .2019. 2019: 20.. .2019. . : .2019. : ,. .2019. ":" Sony Pictures Entertainment You Tube-.24 09:44. . 2. 2. -,:. 10:03 .- ,,,, -. : ,, ,,,,,,,, ,, ,,,,. ,,,,. Alexa: 8,462,430 Google Page Rank: 1 10 … . . . 17:50, 2. "-". . 8:00 p.m. . 20:30. "" 1-4. . 00:20 : (2019) ,:. : 16 .: 13 2019.: ,,. : ,,. : X.: ,. X. NA10. 4. x. NA10. i 2012, for example, i i i 17. 2017, 21 1753 1-5 2019, 5,610. 12. 9 150. 2018 101. 2018 32: i 2019 hd i i 2019 2019 i hd i i 2019 hd 2019 i. . , 1 + 1 ,,,,,,,. ,,,,,, -. . . :: 2019: i: 2019 i :: 2019: i :: 2019 :: http: //bigtombolo.ning.com/profiles/…3tziw871wt6i96.

Quintondum
reviewed by Quintondum in
.
: 2019 ri
: 2019 rihttps: //i106.fastpic*****big/2019/0605/59/d49a0771a1110c83e279a33337fe4659.jpg i: i: i:,:,. Silentium I – .30. 2016: () :: ,,. – 68 000 000.6. . 2019, – .14: 40. 16:40. 19:00:, 13. 2019: .21. 2019 2. International GT Open. I. & # 39; (2019), .31 2019: (2019) .49. . . :,, Four. Five,. ,,, 1.-, (., -79-80., -The relationship in the
Classification: 5

.

w8

BlackHatKings: Proxies and VPN section
Posted by: Davidbendy
Time of publication: June 13, 2019 at 01:03 AM.

How to conditionally map two identical variables in nginx?

I would like to configure the variable $ sub conditionally dependent on $ request_uri Y $ host.

map $ request_uri $ sub {
default front
~ ^ / api /.* api;
~ ^ / rest /.* rest;
}

map $ host $ sub {
host names

#default $ sub; # Tried, unsuccessful

ping * ping;
admin admin
}

server {
listen 80;
server name _;

root / usr / share / nginx / html;

Location / {
add_header X-Sub $ sub;
try_files $ uri $ uri / /index.html;
}
}

I thought that nginx would not overwrite $ sub in map $ host $ sub if the host name is not in the list, but unfortunately it just goes blank $ sub.

So basically it should be like $ host is "ping" or "admin" set $ sub in consecuense. If the host name does not match, verify $ request_uri.

Any idea how to file that statement?

Map controller rumble to Smartphone

Is it possible to assign noise signals from the game controller to smartphones with built-in vibration motor?
I have a Bluetooth driver without the rumble function, so I wanted to map the rumble to the built-in vibration motor on the smartphone. Especially for PC games that I transmit to my phone through Parsec.

javascript – Error using the map () in ReacNative together with the Firebase

I'm new to React-Native and Firebase, and I'm having a hard time bringing bank information (Firebase) to the application through React-Native. I want to look up the names, the schedules and the acronyms, and print everything inside one. in a , forming a list of contents. Then it would look like this:


    Alexandre ... 
    Monday 19:30 ... 
    EA215 ... 



    AndrΓ© ... 
    Monday 17:00 ... 
    EE014  




.
.
.

Note: When I made the code in this way:

let items = Object.keys (date);
// let items2 = Object.values ​​(date);
this.setState ({items});

The code returned the names to me and I could print the names.
And when I used the code in this way:

// let items = Object.keys (date);
let items2 = Object.values ​​(date);
this.setState ({items2});

The code returned to me the schedules and acronyms, that would depend on what I said if it was items2.Sigla_Prof or items2.Profile_Prof

But when I use two elements in this way:

let items = Object.keys (date);
let items2 = Object.values ​​(date);
this.setState ({items, items2});

The error code saying that the this.props.items2.map It is not an object.
Why does this happen? And how can I fix that? How can I have him bring names, schedules and acronyms to me?

firebase

insert the description of the image here

Code 1

insert the description of the image here

Code 2

insert the description of the image here

error

insert the description of the image here

tables – How to describe two variables on a heat map?

I need to describe the distribution of daytime schedules and their occupation.

The distribution of schedules throughout the day can be described using a simple heat / table map, for example.

Showtime distribution

Here, each time cell contains the number of hours in that hour. The color shows what time has more schedules.

How do I add information about the occupation at each hour without losing the current information?

I am considering dividing the cell diagonally, eg.

diagonal division

or move the information out of the table completely to a separate table.

vector spaces: find a matrix of (any) linear map $ varphi: mathbb {R} ^ {4} rightarrow mathbb {R} ^ {3} $

I'm trying to find a matrix of (any) linear map $ varphi: mathbb {R} ^ {4} rightarrow mathbb {R} ^ {3} $, for which the following applies:

  • the dimension of the image $ varphi = 2 $

  • $ varphi (1,1,1,1) = (1,2,1) $

  • $ varphi (1,0,1,0) = (2,1,0) $

I have already determined, that the dimension of the kernel. $ varphi $ will be $ 2 $. What should my next steps be? Thank you!