Second-countable T1 space
Definition
A topological space is termed a second-countable T1 space if it is both a second-countable space and a T1 space.
This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
This article describes a property of topological spaces obtained as a conjunction of the following two properties: second-countable space and T1 space
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Polish space | ||||
| separable metrizable space |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| second-countable space | ||||
| T1 space | ||||
| perfect space | second-countable and T1 implies perfect |