# On absolutely submetrizable spaces

Commentationes Mathematicae Universitatis Carolinae (2006)

- Volume: 47, Issue: 3, page 483-490
- ISSN: 0010-2628

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topBuzyakova, Raushan Z.. "On absolutely submetrizable spaces." Commentationes Mathematicae Universitatis Carolinae 47.3 (2006): 483-490. <http://eudml.org/doc/249858>.

@article{Buzyakova2006,

abstract = {We introduce a notion of absolute submetrizability (= ``every Tychonoff subtopology is submetrizable'') and investigate its behavior under basic topological operations. The main result is an example of an absolutely submetrizable space that contains an uncountable set of isolated points (hence the space is neither separable nor hereditarily Lindelöf). This example is used to show that absolute submetrizability is not preserved by some topological operations, in particular, by free sums.},

author = {Buzyakova, Raushan Z.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {submetrizable; absolutely submetrizable; submetrizable space},

language = {eng},

number = {3},

pages = {483-490},

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

title = {On absolutely submetrizable spaces},

url = {http://eudml.org/doc/249858},

volume = {47},

year = {2006},

}

TY - JOUR

AU - Buzyakova, Raushan Z.

TI - On absolutely submetrizable spaces

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2006

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

VL - 47

IS - 3

SP - 483

EP - 490

AB - We introduce a notion of absolute submetrizability (= ``every Tychonoff subtopology is submetrizable'') and investigate its behavior under basic topological operations. The main result is an example of an absolutely submetrizable space that contains an uncountable set of isolated points (hence the space is neither separable nor hereditarily Lindelöf). This example is used to show that absolute submetrizability is not preserved by some topological operations, in particular, by free sums.

LA - eng

KW - submetrizable; absolutely submetrizable; submetrizable space

UR - http://eudml.org/doc/249858

ER -

## References

top- Engelking R., General Topology, Sigma Series in Pure Mathematics, 6, Heldermann, Berlin, revised ed., 1989. Zbl0684.54001MR1039321
- Mrówka S., On completely regular spaces, Fund. Math. 41 (1954), 105-106. (1954) MR0063650
- Sneider V., Continuous images of Souslin and Borel sets; Metrization theorems, Doklady Akad. Nauk SSSR 50 (1959), 77-79. (1959) MR0053493

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