Peano space

Peano space

In point-set topology, a branch of mathematics, a Peano space, named after Giuseppe Peano, is a compact, connected, locally connected metric space.

Properties

*Every Peano space is arcwise connected, more generally every open connected subset of a Peano space is arcwise connected.
*Hahn-Mazurkiewicz theorem: A Hausdorff space is a continuous image of the unit interval if and only if it is a Peano space.

References

*cite book | author=Wilard, Stephen | title=General Topology | publisher=Dover Publications | year=2004 | id=ISBN 0-486-43479-6


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • space — 1. noun /speɪs/ a) The intervening contents of a volume. If it be only a Single Letter or two that drops, he thruſts the end of his Bodkin between every Letter of that Word, till he comes to a Space: and then perhaps by forcing thoſe Letters… …   Wiktionary

  • Space-filling curve — 3 iterations of a Peano curve construction, whose limit is a space filling curve. In mathematical analysis, a space filling curve is a curve whose range contains the entire 2 dimensional unit square (or more generally an N dimensional hypercube) …   Wikipedia

  • Peano, Giuseppe — (1858–1932)    The son of a peasant family from a small village near Cuneo in Piedmont, Giuseppe Peano was one of the most important mathematicians of his day. He began his university career in 1876 at Turin, where he would continue to work and… …   Historical Dictionary of modern Italy

  • Peano , Giuseppe — (1858–1932) Italian mathematician and logician Peano, who was born at Spinetta near Cuneo, in Italy, studied at the University of Turin and was an assistant there from 1880. He became extraordinary professor of infinitesimal calculus in 1890 and… …   Scientists

  • space-filling curve — noun a curve whose range contains the entire 2 dimensional unit square (or the 3 dimensional unit cube) See Also: Peano curve …   Wiktionary

  • Peano curve — noun A space filling curve in the 2 dimensional plane …   Wiktionary

  • Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …   Wikipedia

  • Giuseppe Peano — Infobox Scientist name = Giuseppe Peano image width = 220px birth date = birth date|1858|8|27 birth place = Spinetta, Piedmont, Italy death date = death date and age|1932|4|20|1858|8|27 residence = Italy citizenship = Italian field = Mathematics… …   Wikipedia

  • Courbe de Peano — Giuseppe Peano Une courbe de Peano est une courbe plane paramétrée par une fonction continue sur l intervalle unité [0, 1], surjective dans le carré [0, 1]×[0, 1], c est à dire que la courbe passe par chaque point du carré : elle… …   Wikipédia en Français

  • vector space — Math. an additive group in which addition is commutative and with which is associated a field of scalars, as the field of real numbers, such that the product of a scalar and an element of the group or a vector is defined, the product of two… …   Universalium

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”