Is 'metric space' a common English term?

No, it is a specialised term used almost exclusively in university-level mathematics, computer science, and theoretical physics.

Can 'metric' in 'metric space' mean 'using the metre'?

No. In this context, 'metric' refers to the mathematical concept of a distance function, not the unit of measurement. The connection is historical, as both relate to measurement.

What's the simplest example of a metric space?

The set of real numbers with the standard distance function d(x, y) = |x - y|. The 2D plane with Euclidean distance is another common example.

How is a metric space different from a topological space?

A metric space is a more specific structure. Every metric space induces a topological space (its 'metric topology'), but not all topological spaces come from a metric. Topological spaces deal with a more general notion of 'closeness' without a numerical distance.

Is “metric space” formal?

Metric space is usually technical / academic (mathematics, computer science) in register.

How do you pronounce “metric space”?

Metric space: in British English it is pronounced /ˈmetrɪk ˌspeɪs/, and in American English it is pronounced /ˈmetrɪk ˌspeɪs/. Tap the audio buttons above to hear it.

metric space: meaning, definition, pronunciation and examples

UK/ˈmetrɪk ˌspeɪs/US/ˈmetrɪk ˌspeɪs/

Technical / Academic (Mathematics, Computer Science)

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Quick answer

What does “metric space” mean?

A set together with a function (a metric) that defines a distance between any two of its elements, providing a formal framework for discussing concepts like convergence and continuity.

Audio

Pronunciation

Definition

Meaning and Definition

A set together with a function (a metric) that defines a distance between any two of its elements, providing a formal framework for discussing concepts like convergence and continuity.

The fundamental object of study in metric topology; any mathematical or conceptual system where a notion of distance is precisely defined and behaves like standard geometric distance.

Dialectal Variation

British vs American Usage

Differences

No significant lexical or spelling differences. Pronunciations may vary slightly.

Connotations

Identical technical meaning. The word 'metric' alone has broader non-mathematical use in American business contexts (e.g., performance metrics), but the compound 'metric space' remains strictly mathematical.

Frequency

Equally rare in general discourse. Slightly higher frequency in UK academic writing due to historical strength in pure analysis.

Grammar

How to Use “metric space” in a Sentence

[metric space] + [preposition 'with' + metric][verb 'define'/'consider'] + [as a metric space][property] + [holds in/for a metric space]

Vocabulary

Collocations

strong

complete metric spacecompact metric spacedefine a metric spaceon a metric spacestructure of a metric space

medium

separable metric spacebounded metric spaceproperties of a metric spaceexample of a metric spacemetric space theory

weak

interesting metric spacestandard metric spacemetric space conceptmetric space approachmetric space is

Examples

Examples of “metric space” in a Sentence

verb

British English

One can metricise a topological space under certain conditions.
The problem is to metricise the given set effectively.

American English

One can metrizate a topological space under certain conditions.
The problem is to metrizate the given set effectively.

adjective

British English

The metric-space properties of continuity and compactness are fundamental.
We need a metric-space viewpoint for this proof.

American English

The metric space properties of continuity and compactness are fundamental.
We need a metric space viewpoint for this proof.

Usage

Meaning in Context

Business

Virtually never used.

Academic

Core term in real analysis, topology, functional analysis, and some areas of computer science (e.g., algorithm analysis).

Everyday

Never used.

Technical

Used precisely in mathematics, theoretical physics, and some computer science papers dealing with distances in data.

Vocabulary

Synonyms of “metric space”

Neutral

distance space

Weak

topological space (broader)geometric space (broader and less precise)

Vocabulary

Antonyms of “metric space”

set without a metricnon-metric spacediscrete space (in a specific technical sense)

Watch out

Common Mistakes When Using “metric space”

Using 'metric space' to mean 'a space measured in metres' (a unit).
Saying 'a metric' instead of 'a metric space'.
Confusing 'metric' with 'metrical' (related to poetic metre).

FAQ

Frequently Asked Questions

: No, it is a specialised term used almost exclusively in university-level mathematics, computer science, and theoretical physics.
: No. In this context, 'metric' refers to the mathematical concept of a distance function, not the unit of measurement. The connection is historical, as both relate to measurement.
: The set of real numbers with the standard distance function d(x, y) = |x - y|. The 2D plane with Euclidean distance is another common example.
: A metric space is a more specific structure. Every metric space induces a topological space (its 'metric topology'), but not all topological spaces come from a metric. Topological spaces deal with a more general notion of 'closeness' without a numerical distance.
: Metric space is usually technical / academic (mathematics, computer science) in register.
: Metric space: in British English it is pronounced /ˈmetrɪk ˌspeɪs/, and in American English it is pronounced /ˈmetrɪk ˌspeɪs/. Tap the audio buttons above to hear it.

Learning

Memory Aids

Mnemonic

Imagine a SPACE (like a car park) where you have a METRE stick (metric) to measure the distance between any two cars. That measured area is your METRIC SPACE.

Conceptual Metaphor

SPACE IS A CONTAINER FOR POINTS; DISTANCE IS A MEASURABLE PATH.

Practice

Quiz

Fill in the gap

A is the most basic structure in which we can rigorously talk about limits and continuity.

Multiple Choice

What is the defining component of a metric space?