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unusual facts about Burnside's lemma


Burnside's lemma

Consequently, this lemma is sometimes referred to as the lemma that is not Burnside's.


Adrian Burnside

Adrian Mark Burnside (born 15 March 1977) is a retired Australian baseball player born in Alice Springs.

Albanvale, Victoria

Due to the recent development of the Cairnlea and Burnside estates, on the southern and eastern borders of Albanvale, native species of frogs have taken advantage and have taken up residence in the new wetlands and lakes.

Antietam Creek

Burnside's Bridge became a major focus of combat as Union forces under General Ambrose Burnside repeatedly tried to capture the bridge from Confederate forces guarding the crossing from a high bluff overlooking the creek.

Aronszajn tree

The existence of Aronszajn trees (=\aleph 1-Aronszajn trees) was proven by Nachman Aronszajn, and implies that the analogue of König's lemma does not hold for uncountable trees.

Battle of Campbell's Station

Following parallel routes, Longstreet and Burnside raced for Campbell's Station, a hamlet where the Concord Road, from the south, intersected the Kingston Road (now called Kingston Pike) to Knoxville.

Burnside Symphony Orchestra

The Burnside Symphony Orchestra is a community orchestra based in the Burnside Council area in Adelaide, South Australia.

Burnside, Canterbury

Burnside contains a central park (Burnside Park), and its two central roads are Memorial Avenue and Greers Road.

Burnside, Otago

It lay on State Highway 1 until the construction of the Dunedin Southern Motorway in the 1990s, but is now bypassed by traffic from central Dunedin.

Camp Nelson Civil War Heritage Park

General Burnside confiscated the house during the war to serve as officers quarters.

David P. Jenkins

During the American Civil War, Jenkins served in Union Army under Generals Grant, Pope, Sherman and Burnside in the Western Theater.

Desmond Ford

While Burnside was a dynamic presenter, Ford's biographer Milton Hook describes him as a fundamentalist (see: historic Adventism), and draws an analogy with a rugged, gung-ho cowboy like a John Wayne character.

Grand Director

Burnside's plan involves blowing up Hoover Dam to rally other groups like the Watchdogs behind him.

Eventually Burnside joins the terrorist group Watchdogs, and captures Barnes to force him to wear his World War II Bucky uniform and become his new Bucky.

Hartford Wanderers RFC

The Hartford Wanderers are sponsored by Ten Penny Ale which is made by Burnside Brewery, Red Rock Tavern, Connecticut Army National Guard, Crispin Hard Cider Company, ProEx Physical Therapy, and BSA Landscaping.

Hazelwood Park, South Australia

After years of effort, the Burnside Council eventually acquired the park in May 1963 after negotiations with the Premier, Sir Thomas Playford.

Henry L. Benning

At the Battle of Antietam, Benning's brigade was a crucial part in the defense of the Confederate right flank, guarding "Burnside's Bridge" across Antietam Creek all morning against repeated Union assaults.

Hensel's lemma

Masayoshi Nagata proved in the 1950s that for any commutative local ring A with maximal ideal m there always exists a smallest ring Ah containing A such that Ah is Henselian with respect to mAh.

Completeness of a ring is not a necessary condition for the ring to have the Henselian property: Goro Azumaya in 1950 defined a commutative local ring satisfying the Henselian property for the maximal ideal m to be a Henselian ring.

History of group theory

The study was continued by F. N. Cole (up to 660) and Burnside (up to 1092), and finally in an early "millennium project", up to 2001 by Miller and Ling in 1900.

Hotelling

Hotelling's lemma: an economic rule relating the supply of a good to the profit of the good's producer

Imakane, Hokkaido

Imakane Junior High School has an exchange program with Burnside High School, Christchurch, New Zealand.

Jacob Eugene Duryée

At the Battle of Antietam, Duryée stalwartly led his regiment from the front as the men tried to take the infamous Burnside's Bridge over Antietam Creek in the face of withering fire from Georgia regiments on the hills on the opposite bank.

Joseph Cushing Edmands

The regiment reached Annapolis, Maryland in December 1861 and was soon assigned to Brig. Gen. Ambrose Burnside's North Carolina Expedition.

Kaikorai Valley

The valley is home to three distinct suburbs: Kaikorai, Bradford, and Kenmure, while a fourth suburb, Burnside, lies at the valley's mouth, close to the junction of Kaikorai Valley Road and the Dunedin Southern Motorway, part of State Highway 1.

Knox County, Tennessee

With the success of Burnside's troops in the Knoxville Campaign, and especially during the decisive Battle of Fort Sanders, Knox County remained under Union control for the duration of the Civil War.

König's theorem

König's lemma (also known as König's infinity lemma), named after Dénes Kőnig

Neighborhoods of Portland, Oregon

It includes Portland's Chinatown, marked by a pair of lions at its entrance at NW 4th Ave. and W Burnside St. and home to the Portland Classical Chinese Garden.

Oka's lemma

In mathematics, Oka's lemma, proved by Kiyoshi Oka, states that in a domain of holomorphy in Cn, the function –log d(z) is plurisubharmonic, where d is the distance to the boundary.

Palaeeudyptes

The other described New Zealand species, P. marplesi, is known from parts of a skeleton, mainly leg bones, from the Middle or Late Eocene Burnside Mudstone (34 to 40 MYA) at Burnside, Dunedin.

Palaeeudyptes marplesi

This species is known from a partial skeleton, mainly leg bones (Otago Museum C.50.25 to C.50.45), recovered from Middle or Late Eocene Burnside Mudstone rocks (34-40 MYA) at Burnside, Dunedin.

Purchase Line School District

It also serves the Boroughs of New Washington, Burnside, Mahaffey, Newburg, and Bell Townshp in Clearfield County.

Quillen's lemma

In contrast to a version of Schur's lemma due to Dixmier, it does not require k to be uncountable.

River Eden, Fife

It flows from Burnside, near the border with Perth & Kinross, then slowly across the Howe of Fife (until drained in the 18th and 19th centuries a flat and waterlogged basin) and through the market town of Cupar to Guardbridge, where it enters the North Sea via the Eden Estuary, an important conservation area for wading birds and a nature reserve.

Samuel L. Pitkin

He would also establish Pitkin Mills in what became the Burnside village of East Hartford that was dominated by various mills.

Schanuel's lemma

In mathematics, especially in the area of algebra known as module theory, Schanuel's lemma, named after Stephen Schanuel, allows one to compare how far modules depart from being projective.

Scheffé’s lemma

Henry Scheffé published a proof of the statement on convergence of probability densities in 1947.

Shephard's lemma

The lemma is named after Ronald Shephard who gave a proof using the distance formula in his book Theory of Cost and Production Functions (Princeton University Press, 1953).

Skatepark

Skate parks, related obstacles/ramps and locations designed for extreme sport utilization have made their way into the media over time, such as with the aforementioned Burnside Skatepark being included in the movie Free Willy.

South Australia Rugby Union

By 1971 clubs included: Army, Adelaide University, Glenelg, Burnside, Elizabeth, Flinders University, North Adelaide, Old Collegians, Onkaparinga, Port Adelaide, Roseworthy College Rams, Salisbury, Southern Suburbs, West Torrens and Woodville.

Thomas Burnside

Burnside was elected as a Democratic-Republican to the Fourteenth Congress to fill the vacancy caused by the death of David Bard and served unil his resignation in April 1816.

Vili Milisits

He left school aged 14 to work at Kazzy's Cake Shop in Burnside, run by fellow countryman Kazzy Ujvari.

What This Country Needs

Strings arranged by Dennis Burnside and performed by the Nashville String Machine.

William Burnside

The central part of Burnside's group theory work was in the area of group representations, where he helped to develop some of the foundational theory, complementing, and sometimes competing with, the work of Ferdinand Frobenius, who began his research in the subject during the 1890s.

Zorn's Law

Zorn's lemma is a proposition used in many areas of theoretical mathematics.

Zorn's lemma

# Banach's extension theorem which is used to prove one of the most fundamental results in functional analysis, the Hahn–Banach theorem

It occurs in the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis, the theorem that every vector space has a basis, Tychonoff's theorem in topology stating that every product of compact spaces is compact, and the theorems in abstract algebra that every nonzero ring has a maximal ideal and that every field has an algebraic closure.


see also