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Canonical static concept record
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A pseudometric space in which zero distance implies equality.
wp-metricnlab-metrictopology-without-tearsEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require only when .
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-metrictopology-without-tearsEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Require every Cauchy sequence to converge.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-complete-metrictopology-without-tearsThis is an authored directed relation from the source endpoint to the target endpoint.
Metric balls of radii give a countable local base at each point.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
wp-metricwp-first-countabletopology-without-tearsThis is an authored directed relation from the source endpoint to the target endpoint.
Distinct points have disjoint sufficiently small metric balls.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
wp-metricwp-separationtopology-without-tearsThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the metric and its induced topology.
Feed several structures into a construction junction and impose compatibility between them.
wp-compact-metrictopology-without-tearsThis is an authored directed relation from the source endpoint to the target endpoint.
Require separability.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-separabletopology-without-tearsThis is an authored directed relation from the source endpoint to the target endpoint.
Open metric balls generate the canonical topology of a metric space.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
wp-metricnlab-metricwp-top-spacenlab-top-spacetopology-without-tearsThis is an authored directed relation from the source endpoint to the target endpoint.
The entourages define the canonical uniformity of a metric space.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
wp-metricnlab-metricwp-uniformnlab-uniformtopology-without-tears