completely normal space: meaning, definition, pronunciation and examples
LowTechnical/Neutral
Quick answer
What does “completely normal space” mean?
In topology, a topological space in which every two separated sets have disjoint neighborhoods (also called hereditarily normal). In general language, a place or area that is entirely ordinary.
Audio
Pronunciation
Definition
Meaning and Definition
In topology, a topological space in which every two separated sets have disjoint neighborhoods (also called hereditarily normal). In general language, a place or area that is entirely ordinary.
A mathematical concept denoting a strong separation property in topological spaces; more loosely, any environment or situation devoid of unusual or abnormal features.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage; both varieties use the same term in technical contexts.
Connotations
In technical contexts, purely mathematical; in general use, may imply a value judgment (e.g., boring, safe, unremarkable).
Frequency
Extremely rare in non-technical discourse; primarily used in mathematical literature.
Grammar
How to Use “completely normal space” in a Sentence
[Subject] is a completely normal space.In a completely normal space, [property holds].One can show that [space] is a completely normal space.Vocabulary
Collocations
Examples
Examples of “completely normal space” in a Sentence
verb
British English
- He tends to space out his lectures with breaks.
- They will space the trees two metres apart.
American English
- She spaced out during the meeting.
- Make sure to space the posts evenly.
adverb
British English
- He was completely exhausted after the marathon.
- She completely forgot about the appointment.
American English
- I completely understand your point.
- The project was completely finished on time.
adjective
British English
- The room had a completely normal appearance.
- It was a normal day at the office.
American English
- Everything seemed completely normal to her.
- We're back to a normal schedule now.
Usage
Meaning in Context
Business
Virtually never used; if encountered, likely in a metaphorical sense (e.g., 'The market is a completely normal space now').
Academic
Primarily in mathematics (topology) textbooks and papers; occasionally in physics or computer science discussing abstract spaces.
Everyday
Rare; might be used humorously or emphatically to describe a very ordinary place (e.g., 'My office is a completely normal space').
Technical
Standard term in topology for a specific separation axiom.
Vocabulary
Synonyms of “completely normal space”
Strong
Neutral
Weak
Vocabulary
Antonyms of “completely normal space”
Watch out
Common Mistakes When Using “completely normal space”
- Using 'completely normal space' to mean 'very ordinary room' in formal writing.
- Confusing it with 'normal space' (which does not imply hereditary normality).
- Misspelling as 'completly normal space'.
- Incorrectly assuming it is a common collocation in everyday English.
FAQ
Frequently Asked Questions
No, it is a specialized term primarily used in mathematical topology. In everyday conversation, it is rare and usually interpreted literally.
Yes, but only in a literal, non-technical sense (e.g., 'a completely normal office space'). This usage is uncommon and not idiomatic.
In topology, a completely normal space (or hereditarily normal) is one in which every subspace is normal, which is a stronger condition than normality itself.
In American English, it is pronounced approximately as /kəmˈpliːtli ˈnɔːrməl speɪs/, with a rhotic 'r' in 'normal'.
In topology, a topological space in which every two separated sets have disjoint neighborhoods (also called hereditarily normal). In general language, a place or area that is entirely ordinary.
Completely normal space is usually technical/neutral in register.
Learning
Memory Aids
Mnemonic
Imagine a space where every separated pair of sets gets their own separate neighborhoods, completely and normally. Think: 'Completely Normal' = 'Can Neatly Partition'.
Conceptual Metaphor
In mathematics: a highly organized, conflict-free zoning system for sets. In everyday language: a blank canvas, the epitome of ordinariness.
Practice
Quiz
What is a synonym for 'completely normal space' in topology?