Category:Separable Spaces
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This category contains results about Separable Spaces in the context of Topology.
A topological space $T = \struct {S, \tau}$ is separable if and only if there exists a countable subset of $S$ which is everywhere dense in $T$.
Subcategories
This category has the following 6 subcategories, out of 6 total.
Pages in category "Separable Spaces"
The following 61 pages are in this category, out of 61 total.
C
- Closed Unit Ball in Normed Dual Space of Separable Normed Vector Space is Weak-* Separable
- Compact Complement Topology is Separable
- Compact Metric Space is Separable
- Condition for Open Extension Space to be Separable
- Continuous Image of Separable Space is Separable
- Countable Complement Space is not Separable
- Countable Discrete Space is Separable
- Countable Excluded Point Space is Separable
- Countable Fort Space is Separable
- Countable Product of Separable Spaces is Separable
- Countable Space is Separable
E
M
N
- Normed Dual of Normed Vector Space is Separable iff Closed Unit Ball is Metrizable
- Normed Dual Space of Separable Normed Vector Space is Weak-* Separable
- Normed Vector Space is Separable iff Weakly Separable
- Normed Vector Space of Bounded Sequences is not Separable
- Normed Vector Space over Complex Numbers with Schauder Basis is Separable
- Normed Vector Space with Schauder Basis is Separable
S
- Second-Countable Space is Separable
- Separability in Uncountable Particular Point Space
- Separability is not Weakly Hereditary
- Separability of Normed Vector Space preserved under Isometric Isomorphism
- Separable Discrete Space is Countable
- Separable Metacompact Space is Lindelöf
- Separable Metric Space is Homeomorphic to Subspace of Fréchet Metric Space
- Separable Metric Space is Second-Countable
- Separable Normed Vector Space Isometrically Isomorphic to Linear Subspace of Space of Bounded Sequence
- Separable Space need not be First-Countable
- Separable Space satisfies Countable Chain Condition
- Separable Topological Space remains Separable in Coarser Topology
- Sequentially Compact Metric Space is Separable
- Space is Separable iff Density not greater than Aleph Zero
- Subspace of Separable Metric Space is Separable