In literature:
Of pure iron springs, the famous Schwalbach contains rather more iron than the Ute Iron, and Spa rather less.
"Over the Rocky Mountains to Alaska" by Charles Warren Stoddard
Leopold took up his quarters at this hotel in his way to Spa.
"Olla Podrida" by Frederick Marryat (AKA Captain Marryat)
It was the group of protection of Spa.
"High Adventure" by James Norman Hall
Saratoga Spa, New England, 24.32.
"The American Missionary - Volume 52, No. 1, March, 1898" by Various
Spa Fields, Bermondsey, 175.
"The Political History of England - Vol XI" by George Brodrick
The poor chap was killed in a duel at Spa, a few months after the marriage.
"The Picture of Dorian Gray" by Oscar Wilde
MacKenzie was in Brussels while they were in Spa.
"The Explorer" by W. Somerset Maugham
The Belgian doctor sent them to the well-known baths at Spa.
"The Son of His Mother" by Clara Viebig
The Grand was overrun by a smartly dressed crowd, and the Spa was a picturesque sight during the morning promenade.
"The Count's Chauffeur" by William Le Queux
If that is not proper at first, I think the best scheme is going to the Spa.
"A Letter Book" by George Saintsbury
A new town hall, including a central spa and assembly rooms, was opened in 1903.
"Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 1" by Various
He managed to escape, but it was proved that the body had been taken from Spa Fields, and Naples was sentenced to two years' imprisonment.
"The Diary of a Resurrectionist, 1811-1812" by James Blake Bailey
We must send them to a foreign spa for a six-weeks' course.
"What a Man Wills" by Mrs. George de Horne Vaizey
It was never a Roman military station, being used apparently solely as a Spa.
"The Towns of Roman Britain" by James Oliver Bevan
The sands were empty at this season, and the Spa unpopulous except for a few residents.
"Plashers Mead" by Compton Mackenzie
Spa was as quiet and retired as Brodie described it.
"Diary And Notes Of Horace Templeton, Esq. Volume I (of II)" by Charles James Lever
At the close of the preceding century, or during the latter half of it, Clifton Spa was the chief attraction.
"Under the Mendips" by Emma Marshall
I walked up and down the Spa-Walk, whiffing a cigar, for a quarter of an hour, without being able to come to a decision.
"Tales from "Blackwood," Volume 3" by Various
I walked up and down the Spa-Walk, whiffing a cigar, for a quarter of an hour, without being able to come to a decision.
"Tales from Blackwood, Volume 3" by Various
The spa is largely frequented in summer and has agreeable public rooms and gardens.
"Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 8" by Various
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In poetry:
She died in the upstairs bedroom
By the light of the ev'ning star
That shone through the plate glass window
From over Leamington Spa
"Death In Leamington" by Sir John Betjeman
Ah, not a word about his ship? Well, well, I'll lay thee by.
I see a heron from the marsh go sailing in the sky,
The purple moor is like a dream, a star is twinkling clear--
Perhaps the meeting that she spaed is drawing very near!
"The Shell" by Isabella Valancy Crawford
So night by night I watch for him--by day I sing and work,
And try to never mind the latch--he's coming in the dark;
Yet as the days and weeks and months go slipping slowly thro',
I wonder if the wise old wife has spaed my fortune true!
"The Shell" by Isabella Valancy Crawford
Here in the gardens of the Spa Pavillion
Warm in the whisper of the summer sea,
The cushioned scabious, a deep vermillion,
With white pins stuck in it, looks up at me
A sun-lit kingdom touched by butterflies
And so my memory of the winter dies.
"Felixstowe, Or The Last Of Her Order" by Sir John Betjeman
In news:
Heritage Bay spa offers decadent treatments.
The staff at Legal Hair and Day Spa in Steubenville looked on as Redken educator Lauren Hagen demonstrates new hair design and coloring techniques during a recent workshop.
Miano Viel Salon and Spa.
Since 1985, this full-service salon and spa has specialized in versatile cuts and natural dye jobs for an upscale clientele of midtown professionals.
Spa Professional Discovers Dharma .
Darryl Webb/For the Star-Ledger Outside of the Westin Kierland Resort & Spa, ALEC attendees take a break during the annual summit in Scottsdale, Ariz. Kraft Foods, Inc and the Coca Cola Co.
The Houstonian Hotel, Club and Spa Need some funding for your new nonprofit group.
BROOKFIELD- She was the target of the killing spree at the spa, and for the very first time, Zina Haughton's family talks about Zina and the tragic end to her life.
The Dragontree Spa in the Portland Airport Celebrates First Anniversary.
Amanda Darbenzio of Manhattan gets a Geisha Facial at Shizuka New York Day Spa.
A Chinese man thought he would look years younger after bathing with live eels in a spa treatment designed to remove dead skin.
The home was designed by Robert Byrd with entertaining in mind, with a spa, park-like grounds and four fireplaces.
Jersey City grants OK for pet-spa owner to build enclosure for dog pool.
Enlarge Michael Dempsey/The Jersey Journal Jersey City Unleashed Pet Resort and Spa have an outdoor pool that dogs can play in.
Borgata Hotel Casino & Spa Launches DRINK PINK for Breast Cancer Awareness Month.
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In science:
Let (R, R+ ) be an aﬃnoid k-algebra, and let X = Spa(R, R+ ).
Perfectoid spaces
The points of Spa(R, R+ ) are in bijection with maps (R, R+ ) → (K, K + ) to complete aﬃnoid ﬁelds (K, K + ) such that the quotient ﬁeld of the image of R in K is dense.
Perfectoid spaces
Let (R, R+ ) be an aﬃnoid k-algebra, and let x, y ∈ X = Spa(R, R+ ) correspond to maps (R, R+ ) → (K, K + ), resp. (R, R+ ) → (L, L+ ).
Perfectoid spaces
Let (R, R+ ) be a perfectoid aﬃnoid K -algebra, and let X = Spa(R, R+ ) with associated presheaves OX , O+ X .
Perfectoid spaces
X = Spa(R, R◦ ), we have |f (x) − g (cid:93) c, (x)| ≤ | |1− max(|f (x)|, | |c ) .
Perfectoid spaces
Note that for < 1, the given estimate says in particular that for all x ∈ X = Spa(R, R◦ ), we have max(|f (x)|, | |c ) = max(|g (cid:93) c, (x)|, | |c ) .
Perfectoid spaces
X = Spa(R, R◦ ), we have |f (x) − g (cid:93) c (x)| ≤ | |1−+(c) max(|f (x)|, | |c ) .
Perfectoid spaces
Proof. (i) As any maximal point of Spa(R, R+ ) is contained in Spa(R, R◦ ), and it is enough to check the inequality at maximal points after increasing slightly, it is enough to prove this if R+ = R◦ .
Perfectoid spaces
Let (S, S+ ) be a reduced aﬃnoid K -algebra of topological ly ﬁnite type, and let X = Spa(S, S+ ).
Perfectoid spaces
Then one checks by hand that Spa(L, L+ ) ∼= lim←− Spa(Ri , R+ i ), compatible with rational subspaces.
Perfectoid spaces
We see that to any perfectoid aﬃnoid K -algebra (R, R+ ), we have associated an aﬃnoid adic space X = Spa(R, R+ ).
Perfectoid spaces
We say that a perfectoid space X (cid:91) over K (cid:91) is the tilt of a perfectoid space X over K if there is a functorial isomorphism Hom(Spa(R(cid:91) , R(cid:91)+ ), X (cid:91) ) = Hom(Spa(R, R+ ), X ) for al l perfectoid aﬃnoid K -algebras (R, R+ ) with tilt (R(cid:91) , R(cid:91)+ ).
Perfectoid spaces
As usual, one reduces to the aﬃne case, X = Spa(A, A+ ), Y = Spa(B , B+ ) and Z = Spa(C, C + ), and we want to construct W = X ×Y Z .
Perfectoid spaces
This is given by W = Spa(D , D+ ), where D is the completion of A ⊗B C , and D+ is the completion of the integral closure of the image of A+ ⊗B+ C + in D .
Perfectoid spaces
In this section, we use the term locally noetherian adic space over k for the adic they are locally of the form Spa(A, A+ ), were spaces over k considered in , i.e. A is a strongly noetherian Tate k-algebra.
Perfectoid spaces
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