Atta Troll ( actually begun in 1841 after a trip to the Pyrenees ) mocks the literary failings Heine saw in the radical poets, particularly Freiligrath.

Old friends like Georg Friedrich Herwegh, who had worked with Marx on the Rheinsche Zeitung, Heinrich Heine, the famous poet, a young doctor by the name of Roland Daniels, Heinrich Bürgers and August Herman Ewerbeck all maintained their contacts with Marx and Engels in Brussels.

On Berlioz's return to Paris, a concert including Symphonie fantastique ( which had been extensively revised in Italy ) and Le retour à la vie was performed, with among others in attendance: Victor Hugo, Alexandre Dumas, Heinrich Heine, Niccolò Paganini, Franz Liszt, Frédéric Chopin, George Sand, Alfred de Vigny, Théophile Gautier, Jules Janin and Harriet Smithson.

Bakunin played a leading role in the May Uprising in Dresden in 1849, helping to organize the defense of the barricades against Prussian troops with Richard Wagner and Wilhelm Heine.

Together with other young men, among them the poet Heinrich Heine, Zunz founded the Verein fur Kultur und Wissenschaft der Juden The Society for the Culture and Science of the Jews alongside Joel Abraham List, Isaac Marcus Jost, and Eduard Gans in Berlin in 1819.

The history of what today is called the Heine – Borel theorem starts in the 19th century, with the search for solid foundations of real analysis.

A & M Heine, her father's firm, helped finance Napoleon III ’ s war with Prussia.

Heine did not find work on the newspaper congenial, and instead tried to obtain a professorship at Munich University, with no success.

Heine reluctantly fell in love with her.

Nevertheless she moved in with Heine in 1836 and lived with him for the rest of his life ( they were married in 1841 ).

Heine regarded Börne, with his admiration for Robespierre, as a puritanical neo-Jacobin and remained aloof from him in Paris, which upset Börne, who began to criticise him ( mostly semi-privately ).

In December Heine met the Marxes and got on well with them.

In the French edition of " Lutetia " Heine wrote, one year before he died: " This confession, that the future belongs to the Communists, I made with an undertone of the greatest fear and sorrow and, oh !, this undertone by no means is a mask!

In October – December 1843 Heine made a journey to Hamburg to see his aged mother and to patch things up with Campe with whom he had had a quarrel.

At the time, Heine was working on two linked but antithetical poems with Shakespearean titles: Deutschland: Ein Wintermärchen (" Germany.

" Liszt then broke relations with Heine.

During these final years Heine had a love affair with the young Camille Selden, who visited him regularly.

Heine on his sickbed, 1851It was probably a similar fatalism that led Meyerbeer never to enter public controversy with those who slighted him, either professionally or personally, although he occasionally displayed his grudges in his Diaries ; for example, on hearing Robert Schumann conduct in 1850: ' I saw for the first time the man who, as a critic, has persecuted me for twelve years with a deadly enmity.

Meyerbeer's relationship with Heine displays the awkwardness and prickliness of the social personas of both parties.

Heine, living in Paris from 1830, always equivocal about his loyalties between Judaism and Christianity, and always short of money, asked Meyerbeer to intervene with Heine's own family for financial support and frequently took loans and money from Meyerbeer himself.

These letters were forwarded to the elder Wyttenbach, with a strong recommendation from Heine.

** Alice Heine, American wife of Albert I of Monaco ( b. 1858 )

Alice Heine ( February 10, 1858 – December 22, 1925 ), styled HSH The Princess of Monaco, and also The Duchess of Richelieu, was the American-born second wife of Prince Albert I of Monaco, a great-grandfather of Prince Rainier III of Monaco.

Heine also made valuable acquaintances in Berlin, notably the liberal Karl August Varnhagen and his Jewish wife Rahel, who held a leading salon.

One of the sons he had with his wife Henriette Ludovike Camerer ( 1807 – 1884, married in 1831 ) was Carl Wilhelm Heine ( 1838 – 1877 ), one of the most famous European surgeons of the 19th Century.

Heine was the first author to introduce the chance of salvation through a woman's devotion and the opportunity to set foot on land every seven years to seek a faithful wife.

That this form of compactness holds for closed and bounded subsets of Euclidean space is known as the Heine – Borel theorem.

The Heine – Borel theorem, as the result is now known, is another special property possessed by closed and bounded sets of real numbers.

Ultimately the Russian school of point-set topology, under the direction of Pavel Alexandrov and Pavel Urysohn, formulated Heine – Borel compactness in a way that could be applied to the modern notion of a topological space.

This follows from the Heine – Borel theorem.

Again from the Heine – Borel theorem, the closed unit ball of any finite-dimensional normed vector space is compact.

# A is closed and bounded ( Heine – Borel theorem ).

This is a generalization of the Heine – Borel theorem, which states that any closed and bounded subspace S of R < sup > n </ sup > is compact and therefore complete.

* 1797 – Heinrich Heine, German poet ( d. 1856 )

by Bernt Heine, T. C. Schadeberg, Ekkehard Wolff, pp. 117 – 28 SUGIA Beiheft 1-2.

Important results include the Bolzano – Weierstrass and Heine – Borel theorems, the intermediate value theorem and mean value theorem, the fundamental theorem of calculus, and the monotone convergence theorem.

The Heine – Borel theorem implies that a Euclidean n-sphere is compact.

* December 13 – Heinrich Heine, German poet ( d. 1856 )

* February 17 – Heinrich Heine, German writer ( b. 1797 )

* Heine, R. E., 1987 " The Role of the Gospel of John in the Montanist controversy ," in Second Century v. 6, pp 1 – 18.

* The Euclidean spaces R < sup >< var > n </ var ></ sup > ( and in particular the real line R ) are locally compact as a consequence of the Heine – Borel theorem.

* Williamson, Kay & Blench, Roger ( 2000 ) ' Niger – Congo ', in Heine, Bernd & Nurse, Derek ( eds.

In the topology of metric spaces the Heine – Borel theorem, named after Eduard Heine and Émile Borel, states:

In fact, the Heine – Borel theorem for arbitrary metric spaces reads:

Émile Borel in 1895 was the first to state and prove a form of what is now called the Heine – Borel theorem.

* Heinrich Heine ( 1797 – 1856 ), German poet

Indeed, the Heine – Borel definition of compactness — that every covering of a space by open sets admits a finite subcovering — is relatively recent.