Spațiu (matematică)

  • Acest articol se referă la conceptul de spațiu din matematică și eventualele sale interpretările sale filozofice.

Pentru alte sensuri, vedeți Spațiu (dezambiguizare).

Spațiul, în matematică, reprezintă o mulțime de elemente (puncte) cu anumite proprietăți.

Definiții

  • Spațiu euclidian (real) n - dimensional, mulțime ale cărei puncte se pot pune în corespondență biunivocă cu sistemele ordonate de n numere reale și în care s-a definit distanța d dintre două puncte x de coordonate (x1, x2, ..., xn) și respectiv y de coordonate (y1, y2, ..., yn) prin formula lui Pitagora:

d ( x , y ) =

  • Spațiu proiectiv, spațiu ale cărui proprietăți sunt invariante față de transformările proiective.
  • spațiu vectorial, numit și spațiu liniar, modul peste un corp de scalari. Exemplu : mulțimea funcțiilor reale continue definite pe un interval [ a, b ], mulțimea matricilor pătrate de ordinul n sunt spații vectoriale peste corpul numerelor reale, complexe. Spațiile vectoriale au fost definite în forma actuală de Giuseppe Peano (1888), dar fondatorul spațiilor vectoriale rămâne Hermann Gunther Grassmann (1844).
  • Spațiu funcțional - spațiu topologic ale cărui elemente sunt funcții. Cele mai importante spații funcționale sunt cele liniare.
  • Spațiul lui Riemann, varietate diferențiabilă, dotată cu o lege de măsurare a lungimilor unor curbe
  • Spațiu conform este un spațiu al lui Riemann având proprietatea că metrica sa, înmulțită cu o funcție depinzând de coordonate, devine metrica spațiului euclidian.

Vezi și

Bibliografie

  • Dicționar de matematici generale, Ed enciclopedică română, București, 1974
  • Mică enciclopedie matematică, Editura Tehnică, București, 1980.

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