# Approximate inverse systems of uniform spaces and an application of inverse systems

Commentationes Mathematicae Universitatis Carolinae (1991)

- Volume: 32, Issue: 3, page 551-565
- ISSN: 0010-2628

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topCharalambous, Michael G.. "Approximate inverse systems of uniform spaces and an application of inverse systems." Commentationes Mathematicae Universitatis Carolinae 32.3 (1991): 551-565. <http://eudml.org/doc/247292>.

@article{Charalambous1991,

abstract = {The fundamental properties of approximate inverse systems of uniform spaces are established. The limit space of an approximate inverse sequence of complete metric spaces is the limit of an inverse sequence of some of these spaces. This has an application to the dimension of the limit space of an approximate inverse system. A topologically complete space with $\operatorname\{dim\} \le n$ is the limit of an approximate inverse system of metric polyhedra of $\operatorname\{dim\} \le n$. A completely metrizable separable space with $\operatorname\{dim\} \le n$ is the limit of an inverse sequence of locally finite polyhedra of $\operatorname\{dim\} \le n$. Finally, a new proof is derived of the important equality $\operatorname\{dim\} = \operatorname\{Ind\}$ for metric spaces.},

author = {Charalambous, Michael G.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {inverse systems; approximate inverse systems; uniform; metric and complete spaces; covering and inductive dimension; covering dimension; inductive dimension; approximate inverse systems; uniform spaces; complete metric spaces; inverse sequence; complete space},

language = {eng},

number = {3},

pages = {551-565},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Approximate inverse systems of uniform spaces and an application of inverse systems},

url = {http://eudml.org/doc/247292},

volume = {32},

year = {1991},

}

TY - JOUR

AU - Charalambous, Michael G.

TI - Approximate inverse systems of uniform spaces and an application of inverse systems

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1991

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 32

IS - 3

SP - 551

EP - 565

AB - The fundamental properties of approximate inverse systems of uniform spaces are established. The limit space of an approximate inverse sequence of complete metric spaces is the limit of an inverse sequence of some of these spaces. This has an application to the dimension of the limit space of an approximate inverse system. A topologically complete space with $\operatorname{dim} \le n$ is the limit of an approximate inverse system of metric polyhedra of $\operatorname{dim} \le n$. A completely metrizable separable space with $\operatorname{dim} \le n$ is the limit of an inverse sequence of locally finite polyhedra of $\operatorname{dim} \le n$. Finally, a new proof is derived of the important equality $\operatorname{dim} = \operatorname{Ind}$ for metric spaces.

LA - eng

KW - inverse systems; approximate inverse systems; uniform; metric and complete spaces; covering and inductive dimension; covering dimension; inductive dimension; approximate inverse systems; uniform spaces; complete metric spaces; inverse sequence; complete space

UR - http://eudml.org/doc/247292

ER -

## References

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