Category:Sequentially Compact Spaces
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This category contains results about Sequentially Compact Spaces.
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$.
Then $H$ is sequentially compact in $T$ if and only if every infinite sequence in $H$ has a subsequence which converges to a point in $S$.
Subcategories
This category has the following 4 subcategories, out of 4 total.
Pages in category "Sequentially Compact Spaces"
The following 33 pages are in this category, out of 33 total.
C
- Closed Unit Ball in Normed Dual Space of Separable Normed Vector Space is Weak-* Sequentially Compact
- Compact Complement Topology is Sequentially Compact
- Compact Subspace of Metric Space is Sequentially Compact in Itself
- Compactness and Sequential Compactness are Equivalent in Metric Spaces
- Complete and Totally Bounded Metric Space is Sequentially Compact
- Composition of Continuous Mapping on Compact Space Preserves Uniform Convergence
- Countable Product of Sequentially Compact Spaces is Sequentially Compact
- Countably Compact First-Countable Space is Sequentially Compact
- Countably Compact Metric Space is Sequentially Compact
E
F
M
S
- Sequential Compactness is Preserved under Continuous Surjection
- Sequentially Compact Metric Space is Compact
- Sequentially Compact Metric Space is Complete
- Sequentially Compact Metric Space is Lindelöf
- Sequentially Compact Metric Space is Second-Countable
- Sequentially Compact Metric Space is Separable
- Sequentially Compact Metric Space is Totally Bounded
- Sequentially Compact Metric Subspace is Sequentially Compact in Itself iff Closed
- Sequentially Compact Space is Countably Compact
- Subset of Indiscrete Space is Compact and Sequentially Compact
- Subset of Indiscrete Space is Sequentially Compact