Geodesic
A study of universal elements in classes of bases of topological spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 62 (2021) no. 4, pp. 491-506.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

The universality problem focuses on finding universal spaces in classes of topological spaces. Moreover, in ``Universal spaces and mappings'' by S. D. Iliadis (2005), an important method of constructing such universal elements in classes of spaces is introduced and explained in details. Simultaneously, in ``A topological dimension greater than or equal to the classical covering dimension'' by D. N. Georgiou, A. C. Megaritis and F. Sereti (2017), new topological dimension is introduced and studied, which is called quasi covering dimension and is denoted by $\dim_{q}$. In this paper, we define the base dimension-like function of the type dim$_{q}$, denoted by {b} - {dim}$^{\rm I F}_{q}$, and study the property of universality for this function. Especially, based on the method of ``Universal spaces and mappings'' by S. D. Iliadis (2005), we prove that in classes of bases which are determined by {b} - {dim}$^{\rm I F}_{q}$ there exist universal elements.
DOI : 10.14712/1213-7243.2021.027
Classification : 54F45
Keywords: topological dimension; universality property; quasi covering dimension 
@article{10_14712_1213_7243_2021_027,
     author = {Georgiou, Dimitris N. and Megaritis, Athanasios C. and Naidoo, Inderasan and Sereti, Fotini},
     title = {A study of universal elements in classes   of bases of topological spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {491--506},
     publisher = {mathdoc},
     volume = {62},
     number = {4},
     year = {2021},
     doi = {10.14712/1213-7243.2021.027},
     mrnumber = {4405819},
     zbl = {07511576},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2021.027/}
}
TY  - JOUR
AU  - Georgiou, Dimitris N.
AU  - Megaritis, Athanasios C.
AU  - Naidoo, Inderasan
AU  - Sereti, Fotini
TI  - A study of universal elements in classes   of bases of topological spaces
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2021
SP  - 491
EP  - 506
VL  - 62
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2021.027/
DO  - 10.14712/1213-7243.2021.027
LA  - en
ID  - 10_14712_1213_7243_2021_027
ER  - 
%0 Journal Article
%A Georgiou, Dimitris N.
%A Megaritis, Athanasios C.
%A Naidoo, Inderasan
%A Sereti, Fotini
%T A study of universal elements in classes   of bases of topological spaces
%J Commentationes Mathematicae Universitatis Carolinae
%D 2021
%P 491-506
%V 62
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2021.027/
%R 10.14712/1213-7243.2021.027
%G en
%F 10_14712_1213_7243_2021_027
Georgiou, Dimitris N.; Megaritis, Athanasios C.; Naidoo, Inderasan; Sereti, Fotini. A study of universal elements in classes   of bases of topological spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 62 (2021) no. 4, pp. 491-506. doi : 10.14712/1213-7243.2021.027. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2021.027/

Cité par Sources :