totally bounded space
uniform space which has finite covers consisting of "arbitrarily small" sets
Facts
6 properties- Subclass of
- uniform space[1]
- Defining formula
- \forall E\in\mathcal E\exists n\in\mathbb N\exists X_1,\dots,X_n\subseteq X\colon\bigcup_{i=1}^nX_i=X\land X_1^2,\dots,X_n^2\subseteq E[3]
- In defining formula
- E[8]
- Maintained by WikiProject
- WikiProject Mathematics[7]
- Said to be the same as
- proximity space[2]
- Studied by
- metric geometry, general topology, functional analysis[4][5][6]
🏷️ Also known as
en totally bounded space
cs Totálně omezený metrický prostor
de Total beschränkt
de Totalbeschränktheit
de Totalbeschränkt
de Präkompakt
es espacio totalmente acotado
fr espace précompact
fr espace precompact
fr espace totalement borné
fr précompact
he חסום כליל
he מרחב חסום כליל
he מרחב חסום לחלוטין
he קבוצה חסומה כליל
it spazio totalmente limitato
ja 全有界空間
ko 전컴팩트
ko 완전유계
ko 프리컴팩트
🔖 Identifiers · 3
- Freebase ID
- /m/0586zk
- Microsoft Academic ID (discontinued)
- 178771509
- NLab ID
- totally bounded space
🔗 Connections
Studied by 2
Maintained by WikiProject 1
Subclass of 1
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