To see this, note that if L is any algebraic extension of K, then the algebraic closure of L is also an algebraic closure of K, and so L is contained within the algebraic closure of K.

The algebraic closure of K is also the smallest algebraically closed field containing K,

It also led to the closure of several local support and satellite businesses, such as the nearby British Steel Clydesdale Works in Mossend, Clyde Alloy in Netherton and equipment maker Anderson Strathclyde.

In 1879, amid talks surrounding the closure of the university due to its dire financial situation, a wealthy New York publisher with Nova Scotia roots, George Munro, who was also the brother-in-law of Dalhousie's Board of Governors member John Forrest, began to donate to the university.

Increasing debates and influence by NGOs and communities appealed for a new program which would have had included also a disadvantaged communities, and would have had worked towards sustainable development even after mine closure ( included transparency and revenue management ).

The St Helena Church News was published from 1888, the Parish Magazine from 1889, the Diocesan Magazine from 1901 and the Jamestown Monthly from 1912 The latter was renamed the St Helena Church Magazine and was published until 1945 by Canon Wallcot, who extended news coverage from church matters to also include island news after the closure of the St Helena Guardian.

The terms " make " for closure of contacts and " break " for opening of contacts are also widely used.

* English Renaissance theatre – also known as early modern English theatre, refers to the theatre of England, largely based in London, which occurred between the Reformation and the closure of the theatres in 1642.

" The accused may also request a closure of the trial ; though, it must be demonstrated that “ first, there is a substantial probability that the defendant's right to a fair trial will be prejudiced by publicity that closure would prevent, and second, reasonable alternatives to closure cannot adequately protect the defendant's right to a fair trial.

To achieve these goals, Boehm adapted a system of axle-mounted keys with a series of " open rings " ( called brille, German for " eyeglasses ", as they resembled the type of eyeglass frames common during the 19th century ) that were fitted around other tone holes, such that the closure of one tone hole by a finger would also close a key placed over a second hole.

English Renaissance theatre, also known as early modern English theatre, refers to the theatre of England, largely based in London, which occurred between 1567, when the first English theatre ' The Red Lion ' was opened ; and the closure of the theatres in 1642.

Book closure Date Whenever a company announces a dividend pay-out, it also announces a date on which the company will ideally temporarily close its books for fresh transfers of stock.

( Sometimes you will also see an axiom called " closure ", stating that x * y belongs to the set A whenever x and y do.

The intersection property also allows one to define the closure of a set A in a space X, which is defined as the smallest closed subset of X that is a superset of A.

They usually also have a built in closure such as velcro or snaps that is used to secure the diaper onto the baby.

Note that these properties are also satisfied if " interior ", " subset ", " union ", " contained in ", " largest " and " open " are replaced by " closure ", " superset ", " intersection ", " which contains ", " smallest ", and " closed ", respectively.

* In computer science, the asterisk is used in regular expressions to denote zero or more repetitions of a pattern ; this use is also known as the Kleene star or Kleene closure after Stephen Kleene.

Expropriation of Church property and the conditions of state control imposed on the Orthodox Theological School of Halki that have led to its closure by the Patriarchate, are also cited by human rights groups.

These signs are also used to display general messages such as accident, crash, road closure, road works etc.

In computer science, a closure ( also lexical closure or function closure ) is a function or reference to a function together with a referencing environment — a table storing a reference to each of the non-local variables

Telstra deployed a CDMA network, which did not suffer this limitation, and while the AMPS network was closed down at the end of 1999 in the major cities, the closure deadline was extended until the end of 2000 in rural areas to ease the transition to CDMA.

The causeway is generally open from about 3 hours after high tide until 2 hours before the next high tide, but the period of closure may be extended during stormy weather.

Every binary relation R on a set S can be extended to a preorder on S by taking the transitive closure and reflexive closure, R < sup >+=</ sup >.

Later, the closure was extended an additional block to the east to 15th Street, and East Executive Avenue, a small street between the White House and the Treasury Building.

A large drop has since taken place in the Palestinian population in H2, identified with the impact of extended curfews, strict restrictions on movement with 16 check-points in place, the closure of Palestinian commercial activities near settler areas, and settler harassment.

Redwood's policies were tax cuts, reduced public spending, opposing the closure of popular local hospitals, Britain's non-participation in a Single Currency, extended right-to-buy public housing schemes, keeping the Royal Yacht Britannia, and carrying on with the Northern Ireland peace process.

Hong Kong school closure was extended by two weeks to April 21.

On April 5, the Singapore government announced that school closure will be extended.

As a self-contained section of the London Underground closed at weekends and for extended periods during weekdays, Aldwych station before its closure and the branch from Holborn were popular locations for filming scenes set on the Tube.

Occasionally it may have an extended edition if there is an especially eventful event in the news-as happened on 7 July 2011, when closure of the News of the World led to an extended version which went on until 11: 35 pm.

The employed locking systems make an accidental closure during use of an extended tool unlikely.

This restriction remained until 1 June 2010, when broadcast time was extended until 1am each day, following the closure of the Virgin1 + 1 channel on Freeview.

In 1962 the closure was " half disguised " as an extended holiday closure, but the road has remained closed since.

Beaudesert Rail had also been trading while insolvent, resulting in the closure of several local business who had extended them credit.

In addition, because sister show Millennium was cancelled in 1999 without concluding any of the shows extended plot lines, Chris Carter felt he needed to bring closure for his cancelled show.

The licence was re-advertised by the Independent Broadcasting Authority The extended license, now to include Southampton and Winchester, was won by Ocean Sound Ltd. Radio Victory ceased operations in June 1986, a couple of weeks earlier than the expiry date of its franchise, with a test transmission informing listeners of the closure.

After three years of closure threats by the Ministry of Defence and extended negotiations with Carlisle Council, the RAF Carlisle base was finally closed in September 1996, and stood unused for several years.

However, a six-hour daily closure period applies to new licences ( and extended hours authorisations ) granted from 30 October 2008 ; this period is nominated depending on individual and community circumstances.

Following the closure Volk's original electric railway was extended from Paston Place ( today's Halfway ) to Black Rock.

Its coverage area was expanded to the rest of Clwyd in October 1981 and the station was subsequently renamed BBC Radio Clwyd, broadcasting extended local news bulletins, a mid-morning show and occasional special programming from studios in Mold until its closure in October 1993.

Following the closure of the Eurostar Terminal at Waterloo, the police station closed in February 2009, and the railway station is now policed from a new Inner London Police Station a few yards from Waterloo at Holmes Terrace.

Following a period of closure during 1993 when the line was converted to use the four rail electrical system of the London Underground, the ownership of Waterloo & City line was transferred to the Underground on 1 April 1994.

By the time Wolves slid into the Fourth Division in 1986, the John Ireland Stand and the South Bank terrace were the only sections of the ground in use, after new safety laws implemented following the Bradford City stadium fire forced the closure of the North Bank and Waterloo Road Stand, which were very dilapidated.

Until the closure of the Swanage branch, a small number of through 4TC workings to / from Waterloo were operated, also using class 33 / 1 locomotives in similar style to the Weymouth trains.

In 2004, while the Waterloo Region District School Board was planning to build Huron Heights in Southwest Kitchener, the school was supposedly better suited for closure when at a meeting regarding the pending closure of Kitchener-Waterloo Collegiate and Vocational School ( KCI ) a delegate from KCI stated that the Eastwood students and community had not rallied around their school as had KCI and Southwood Secondary School, another school scheduled for closure.