semi-metric space
- noun
- Specialized
:
espacio semi-métrico
- In a semi-metric space, it is possible for two different points to have zero distance between them.
Examples
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A semi-metric space can have distinct points with zero distance.
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The definition of a semi-metric space relaxes one of the conditions required for a true metric space.
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Some problems in topology utilize the concept of a semi-metric space to study convergence.
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The concept of a semi-metric space is important in topology.
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In a semi-metric space, two different points can have a distance of zero between them, challenging our usual understanding of distance.
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The properties of a semi-metric space allow for unique approaches to analyzing functions and their limits in mathematical topology.
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Understanding a semi-metric space is crucial for advanced studies in topology, where distance can behave in unexpected ways.
Synonyms
A space where different points can have distance zero
Surface Forms
Morphology
semi-metric + space
The compound transparently signals a relation to a 'metric' (distance/measurement) and 'space', with the prefix 'semi-' indicating a partial or weakened form, so a learner who knows the constituents can infer it is a kind of metric-like space with relaxed properties. However, the exact technical detail (that distinct points may have zero distance) is specialized and not fully predictable from the parts alone, making the meaning only partially derivable.
Etymology
The name semi-metric space comes from joining semi- meaning 'partly', metric meaning 'measure of distance', and space meaning 'place'. It describes a 'place' where distances behave like usual except two different points can have zero distance, so it is only 'partly' a full metric space.
