Category:First-Countable Spaces
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This category contains results about First-Countable Spaces.
A topological space $T = \struct {S, \tau}$ is first-countable or satisfies the First Axiom of Countability if and only if every point in $S$ has a countable local basis.
Subcategories
This category has the following 2 subcategories, out of 2 total.
Pages in category "First-Countable Spaces"
The following 34 pages are in this category, out of 34 total.
A
C
- Compact Complement Topology is First-Countable
- Compact First-Countable Space is Sequentially Compact
- Condition for Open Extension Space to be First-Countable
- Countable Complement Space is not First-Countable
- Countable Product of First-Countable Spaces is First-Countable
- Countably Compact First-Countable Space is Sequentially Compact
E
F
- First-Countability is Hereditary
- First-Countability is not Continuous Invariant
- First-Countability is Preserved under Open Continuous Surjection
- First-Countable Space is Hausdorff iff All Convergent Sequences have Unique Limit
- First-Countable Space is Sequentially Compact iff Countably Compact
- Fortissimo Space is not First-Countable