An example of a non-topologizable algebra

R. Frankiewicz; G. Plebanek

Studia Mathematica (1995)

  • Volume: 116, Issue: 1, page 85-87
  • ISSN: 0039-3223

Abstract

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We present an example of an algebra that is generated by ω 1 elements, and cannot be made a topological algebra. This answers a problem posed by W. Żelazko.

How to cite

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Frankiewicz, R., and Plebanek, G.. "An example of a non-topologizable algebra." Studia Mathematica 116.1 (1995): 85-87. <http://eudml.org/doc/216221>.

@article{Frankiewicz1995,
abstract = {We present an example of an algebra that is generated by $ω_1$ elements, and cannot be made a topological algebra. This answers a problem posed by W. Żelazko.},
author = {Frankiewicz, R., Plebanek, G.},
journal = {Studia Mathematica},
keywords = {non-topologizable algebra},
language = {eng},
number = {1},
pages = {85-87},
title = {An example of a non-topologizable algebra},
url = {http://eudml.org/doc/216221},
volume = {116},
year = {1995},
}

TY - JOUR
AU - Frankiewicz, R.
AU - Plebanek, G.
TI - An example of a non-topologizable algebra
JO - Studia Mathematica
PY - 1995
VL - 116
IS - 1
SP - 85
EP - 87
AB - We present an example of an algebra that is generated by $ω_1$ elements, and cannot be made a topological algebra. This answers a problem posed by W. Żelazko.
LA - eng
KW - non-topologizable algebra
UR - http://eudml.org/doc/216221
ER -

References

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  1. [1] R. Frankiewicz and P. Zbierski, Hausdorff Gaps and Limits, North-Holland, Amsterdam, 1994. Zbl0821.54001
  2. [2] V. Müller, On topologizable algebras, Studia Math. 99 (1991), 149-153. Zbl0764.46046
  3. [3] W. Żelazko, Selected Topics in Topological Algebras, Aarhus Univ. Lecture Notes 31, 1971. Zbl0221.46041
  4. [4] W. Żelazko, Example of an algebra which is non-topologizable as a locally convex algebra, Proc. Amer. Math. Soc. 110 (1990), 947-949. Zbl0727.46025
  5. [5] W. Żelazko, On topologization of countably generated algebras, Studia Math. 112 (1994), 83-88. Zbl0832.46042

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