10 ENGLISH BOOKS RELATING TO «ULTRAFILTER»
Discover the use of
ultrafilter in the following bibliographical selection. Books relating to
ultrafilter and brief extracts from same to provide context of its use in English literature.
1
Problems and Theorems in Classical Set Theory
If U is an ultrafilter on uj and 0 = no < n\ < • • • are arbitrary natural numbers, then
there exists an A G U with An [ni, n^i) = 0 for infinitely many i < uj. 6. If U is an
ultrafilter on uj, then W contains a set icwof lower density zero. 7. There is an ...
Peter Komjath, Vilmos Totik, 2006
2
Introduction to Set Theory, Third Edition, Revised and Expanded
2.1 Definition A filter U on S is an ultrafilter if for every X C 5, either X € U orS-X€U
. The dual notion is a prime ideal: 2.2 Definition An ideal I on 5 is a prime ideal if
for every X C 5, either 2.3 Lemma A filter F on S is an ultrafilter if and only if it is a
...
Karel Hrbacek, Thomas Jech, 1999
5.29 Corollary. If A is a nonempty set, A belongs to some ultrafilter. Proof. {A} is
then a f-basis and hence must be contained in some ultrafilter. D EXAMPLE OF,
AND REMARKS ON, ULTRAFILTERS. (1) The principal filter at x is an ultrafilter.
4
Handbook of Modal Logic
Ultrafilter. frames. Now let us see how to remove the restriction to finite structures
on the algebra side of (11); our first goal is to represent arbitrary (that is, not
necessarily finite or even atomic) algebras by frames. But, given a bao A, what to
take ...
Patrick Blackburn, Johan F.A.K. van Benthem, Frank Wolter, 2006
Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students.
6
A Course in Model Theory: An Introduction to Contemporary ...
Then /, n Ii = I,(ji,i £ I,; B is closed under finite intersections and does not contain 0
. It is therefore a filter base. The filter FB, or one of its close relatives, often
appears in model theory. An ultrafilter is defined as a maximal filter. Theorem 4.1.
7
An Invitation to Operator Theory
If F is an ultrafilter. then for any subset A of A either A e F or (exclusively) Ac e F .
It is not difficult to see that if U is an ultrafilter and (LEA A ^ 0, then there exists a
unique point 6 C A such that U= {^C A: 6tA}. Any ultrafilter of the above form is ...
8
Infinite Dimensional Analysis: A Hitchhiker's Guide
A filter U is an ultrafilter if U has no proper subfilter. That is, U is an ultrafilter if
u c g for a filter S implies U = S. 2.19 Ultrafilter Theorem Every filter is included in
at least one ultrafilter. Consequently, every infinite set has a free ultrafilter.
Charalambos D. Aliprantis, Kim C. Border, 2007
9
Filters and Filtration Handbook
ULTRADEPTH II — Sterile filters for gases— ultrafilter international
ULTRADRAIN — Condensate drains — ultrafilter international ULTRADRI—
Water separator — ultrafilter international ULTRAIR — Oil removal filter —
ultrafilter international ...
T. Christopher Dickenson, 1997
10
General Topology: Chapters 1-4
It is straightforward to check that a is a filter on X, and (A) is strictly finer than if,
since Bea; but this contradicts the hypothesis that g is an ultrafilter. COROLLARY.
If the union of a finite sequence (A;)^;^„ of subsets of X belongs to an ultra/liter g,
...
10 NEWS ITEMS WHICH INCLUDE THE TERM «ULTRAFILTER»
Find out what the national and international press are talking about and how the term
ultrafilter is used in the context of the following news items.
Ultrafilter ska säkra göteborgarnas vatten
Ultrafilter används för att rena vatten från smuts och bakterier. I stora rör packas ultrafiltren som egentligen är pyttesmå spagettiliknande rör som vattnet måste ... «Sveriges Radio, Jun 15»
Dow's new ultrafilter bags innovation award
Dow's Water & Process Solutions has launched its latest industrial and municipal ultrafiltration water treatment modules at the recent Aquatech conference ... «desalination.biz, Jun 15»
SeeThruEquity Initiates Coverage on Nephros, Inc. (OTCBB: NEPH …
"Nephros has developed an advanced high performance line of filters, called ultrafilters, which are primarily used in dialysis centers for the removal of biological ... «Baystreet.ca, Jun 15»
Nephros Reports 2014 Fourth Quarter and Full Year Financial Results
The decrease is attributable to an inventory reserve expense related to the 2013 recall of our point of use and DSU ultrafilters. Research and development ... «Business Wire, Apr 15»
Everpure Self-Cleaning Filtration System Addresses High-Volume …
It offers the same high capacity and high flow water treatment capabilities as the standard Endurance solution, but features a self-cleaning ultrafilter for ... «Vending Times, Mar 15»
Waiblingen: Ohne Ultrafilter bleibt kein Auge heil
WaiblingenSonnenfinsternis: Ohne Ultrafilter bleibt kein Auge heil. Uwe Roth, vom 18.03.2015 00:00 Uhr. Die Sternwarte Welzheim ist bei wolkenlosem Himmel ... «Zeitungsverlag Waiblingen, Mar 15»
Nephros Provides Corporate Update
In addition, the company also requested, for the DSU in-line ultrafilter, that ... We have launched our NanoGuard-D and NanoGuard-S in-line ultrafilters for the ... «MarketWatch, Mar 14»
Membranteknik för säkrare dricksvatten
Ultrafilter är en del av membrantekniken och inkluderar filter med porer av storlekar alltifrån mikrometer ner till nanometer, det vill säga säga 0,000001 mm eller ... «MyNewsdesk, Jan 14»
Donaldson sells Ultratroc air dryer business
Under the terms of the agreement, Donaldson will continue selling Ultratroc's compressed air dryers and will retain the naming rights to the Donaldson Ultrafilter ... «Filtration + Separation, Aug 13»
Donaldson Company Reaches Definitive Agreement to Sell Ultratroc …
... Donaldson will continue selling Ultratroc's compressed air dryers and will retain the naming rights to the brand names “Donaldson Ultrafilter” and “Ultrafilter. «EON: Enhanced Online News, Aug 13»
