Sanakirja.org

Määritelmät

Substantiivi

1. (countable) That which covers or conceals; a cover; something spread or laid over or wrapped about another.
2. (uncountable) Action of the verb to cover.
3. (topology, of a given open set U) A collection of sets ${\displaystyle \{U_{i}\}}$ such that their union contains ${\displaystyle U}$; such a collection with the additional property that every ${\displaystyle U_{i}}$ is open; such a collection with the additional property that every ${\displaystyle U_{i}}$ is contained in ${\displaystyle U}$.
4. (topology) A special kind of map that establishes a relationship between two topological spaces in the sense that, under the action of the map, the one looks locally like several copies of the second: Formally, a continuous map ${\displaystyle \pi :E\rightarrow X}$ between topological spaces such that there exists, for every point ${\displaystyle x}$ in ${\displaystyle X}$, a discrete space ${\displaystyle D_{x}}$ and an open neighborhood ${\displaystyle U}$ of ${\displaystyle x}$ such that ${\displaystyle \pi ^{-1}(U)=\displaystyle \bigsqcup _{d\in D_{x}}V_{d}}$ and π|_{V_d}:V_d \rightarrow U is a homeomorphism for every ${\displaystyle d\in D_{x}}$. See