Category:Open Sets
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This category contains results about open sets in the context of topology.
Definitions specific to this category can be found in Definitions/Open Sets.
Let $T = \struct {S, \tau}$ be a topological space.
Then the elements of $\tau$ are called the open sets of $T$.
Thus:
- $U \in \tau$
and:
- $U$ is open in $T$
are equivalent statements.
Subcategories
This category has the following 9 subcategories, out of 9 total.
C
- Clopen Sets (15 P)
M
O
- Open Ball is Open Set (4 P)
- Open Sets (Metric Spaces) (15 P)
R
- Regular Open Sets (4 P)
S
Pages in category "Open Sets"
The following 42 pages are in this category, out of 42 total.
C
- Catesian Product of Open Real Intervals is Open in Real Number Plane
- Characterization of Open Set by Open Cover
- Closed Real Interval is not Open Set
- Closure of Open Real Interval is Closed Real Interval
- Closure of Open Set of Closed Extension Space
- Closure of Open Set of Particular Point Space
- Complement of Closed Set is Open Set
- Complement of Lower Closure of Element is Open in Scott Topological Ordered Set
- Continuous Mapping on Union of Open Sets
I
O
- Open and Closed Sets in Multiple Pointed Topology
- Open Ball is Open Set
- Open iff Upper and with Property (S) in Scott Topological Lattice
- Open Real Interval is Open Set
- Open Real Interval is Open Set/Corollary
- Open Real Interval is Regular Open
- Open Set Disjoint from Set is Disjoint from Closure
- Open Set is G-Delta Set
- Open Set Less One Point is Open
- Open Set Less One Point is Open/Corollary
- Open Set minus Closed Set is Open
- Open Sets in Real Number Line