Euclidean topology
In mathematics, and especially general topology, the Euclidean topology is the natural topology induced on Euclidean n-space by the Euclidean metric.
In any metric space, the open balls form a base for a topology on that space.[1] The Euclidean topology on is then simply the topology generated by these balls. In other words, the open sets of the Euclidean topology on are given by (arbitrary) unions of the open balls defined as , for all and all , where is the Euclidean metric.
Properties
- The real line, with this topology, is a T5 space. Given two subsets, say A and B, of R with A ∩ B = A ∩ B = ∅, where A denotes the closure of A, there exist open sets SA and SB with A ⊆ SA and B ⊆ SB such that SA ∩ SB = ∅.[2]
gollark: DO NOT use Visual Basic.
gollark: I don't know if it allows globs. Perhaps you could make a script which thingies the playlist file and then launches VLC.
gollark: If you have an ext4/f2fs filesystem it is also possible to use their built-in encryption support but it leaks file sizes and directory structure.
gollark: I don't know if you can expand volumes encrypted with it but generally the standard for disk encryption on Linux is LUKS.
gollark: Do you want to do full disk encryption or just a data partition?
References
- Metric space#Open and closed sets.2C topology and convergence
- Steen, L. A.; Seebach, J. A. (1995), Counterexamples in Topology, Dover, ISBN 0-486-68735-X
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.