Submetrizable 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 is a variation of metrizability. View other variations of metrizability
Definition
Symbol-free definition
A topological space is said to be submetrizable if we can choose a coarser topology on the space and thus make it a metrizable space.
Relation with other properties
Stronger properties
Metaproperties
Products
This property of topological spaces is closed under taking arbitrary products
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This follows from the fact that a direct product of metrizable spaces is metrizable.
Refining
This property of topological spaces is preserved under refining, viz, if a set with a given topology has the property, the same set with a finer topology also has the property
View all refining-preserved properties of topological spaces OR View all coarsening-preserved properties of topological spaces
This follows immediately from the definition.