Category:Disconnected Spaces
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This category contains results about Disconnected Spaces.
Definitions specific to this category can be found in Definitions/Disconnected Spaces.
Let $T = \struct {S, \tau}$ be a topological space.
Definition $1$
$T$ is disconnected if and only if $T$ is not connected.
Definition $2$
$T$ is disconnected if and only if there exist non-empty open sets $U, V \in \tau$ such that:
- $S = U \cup V$
- $U \cap V = \O$
That is, if there exists a partition of $S$ into open sets of $T$.
Subcategories
This category has the following 10 subcategories, out of 10 total.
C
- Cut Points (1 P)
D
- Disconnected Sets (1 P)
E
P
- Punctiform Spaces (2 P)
S
T
- Totally Separated Spaces (11 P)
Z
Pages in category "Disconnected Spaces"
The following 4 pages are in this category, out of 4 total.