Geodesic
Relationship among various Vietoris-type and microsimplicial homology theories
Archivum mathematicum, Tome 57 (2021) no. 3, pp. 131-150.

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

In this paper, we clarify the relationship among the Vietoris-type homology theories and the microsimplicial homology theories, where the latter are nonstandard homology theories defined by M.C. McCord (for topological spaces), T. Korppi (for completely regular topological spaces) and the author (for uniform spaces). We show that McCord’s and our homology are isomorphic for all compact uniform spaces and that Korppi’s and our homology are isomorphic for all fine uniform spaces. Our homology shares many good properties with Korppi’s homology. As an example, we outline a proof of the continuity of our homology with respect to uniform resolutions. S. Garavaglia proved that McCord’s homology is isomorphic to Vietoris homology for all compact topological spaces. Inspired by this result, we prove that our homology is isomorphic to uniform Vietoris homology for all precompact uniform spaces and that Korppi’s homology is isomorphic to normal Vietoris homology for all pseudocompact completely regular topological spaces.
DOI : 10.5817/AM2021-3-131
Classification : 54J05, 55N05, 55N35
Keywords: McCord homology; Korppi homology; $\mu $-homology; Vietoris homology; nonstandard analysis 
@article{10_5817_AM2021_3_131,
     author = {Imamura, Takuma},
     title = {Relationship among various {Vietoris-type} and microsimplicial homology theories},
     journal = {Archivum mathematicum},
     pages = {131--150},
     publisher = {mathdoc},
     volume = {57},
     number = {3},
     year = {2021},
     doi = {10.5817/AM2021-3-131},
     mrnumber = {4306173},
     zbl = {07396179},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2021-3-131/}
}
TY  - JOUR
AU  - Imamura, Takuma
TI  - Relationship among various Vietoris-type and microsimplicial homology theories
JO  - Archivum mathematicum
PY  - 2021
SP  - 131
EP  - 150
VL  - 57
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2021-3-131/
DO  - 10.5817/AM2021-3-131
LA  - en
ID  - 10_5817_AM2021_3_131
ER  - 
%0 Journal Article
%A Imamura, Takuma
%T Relationship among various Vietoris-type and microsimplicial homology theories
%J Archivum mathematicum
%D 2021
%P 131-150
%V 57
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2021-3-131/
%R 10.5817/AM2021-3-131
%G en
%F 10_5817_AM2021_3_131
Imamura, Takuma. Relationship among various Vietoris-type and microsimplicial homology theories. Archivum mathematicum, Tome 57 (2021) no. 3, pp. 131-150. doi : 10.5817/AM2021-3-131. http://geodesic.mathdoc.fr/articles/10.5817/AM2021-3-131/

Cité par Sources :