On absolutely submetrizable spaces
Commentationes Mathematicae Universitatis Carolinae (2006)
- Volume: 47, Issue: 3, page 483-490
- ISSN: 0010-2628
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Abstract
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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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