Quasi Locally Connected Spaces and Pseudo Locally Connected Spaces
Commentationes Mathematicae, Tome 50 (2010) no. 2.

Voir la notice de l'article dans European Digital Mathematics Library

Two new generalizations of locally connected spaces called ‘quasi locally connected spaces’ and ‘pseudo locally connected spaces’ are introduced and their basic properties are studied. The class of quasi locally connected spaces properly contains the class of almost locally connected spaces (J. Austral. Math. Soc. 31(1981), 421–428) and is strictly contained in the class of pseudo locally connected spaces which in its turn is properly contained in the class of sum connected spaces (Math. Nachrichten 82(1978), 121-129; Ann. Acad. Sci. Fenn. A I Math. 3(1977), 185–205). Product and subspace theorems for quasi (pseudo) locally connected spaces are discussed. Their preservation under mappings and their interplay with mappings are outlined. Function spaces of quasi (pseudo) locally connected spaces are considered. Change of topology of a quasi (pseudo) locally connected space is considered so that it is simply a locally connected space in the coarser topology. In contradistinction with almost locally connected spaces, quasi (pseudo) locally connected spaces constitute a coreflective subcategory of TOP.
Mots-clés : almost (quasi, pseudo) locally connected space, regular open set, regular $F_\sigma $-set, $\theta $-open set, $D_\delta $-completely regular space, quasi $\theta $-continuous function, coreflective subcategory 
@article{COMA_2010__50_2_291991,
     author = {J.K. Kohli and D. Singh and B. K. Tyagi},
     title = {Quasi {Locally} {Connected} {Spaces} and {Pseudo} {Locally} {Connected} {Spaces}},
     journal = {Commentationes Mathematicae},
     publisher = {mathdoc},
     volume = {50},
     number = {2},
     year = {2010},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/COMA_2010__50_2_291991/}
}
TY  - JOUR
AU  - J.K. Kohli
AU  - D. Singh
AU  - B. K. Tyagi
TI  - Quasi Locally Connected Spaces and Pseudo Locally Connected Spaces
JO  - Commentationes Mathematicae
PY  - 2010
VL  - 50
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/COMA_2010__50_2_291991/
LA  - en
ID  - COMA_2010__50_2_291991
ER  - 
%0 Journal Article
%A J.K. Kohli
%A D. Singh
%A B. K. Tyagi
%T Quasi Locally Connected Spaces and Pseudo Locally Connected Spaces
%J Commentationes Mathematicae
%D 2010
%V 50
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/COMA_2010__50_2_291991/
%G en
%F COMA_2010__50_2_291991
J.K. Kohli; D. Singh; B. K. Tyagi. Quasi Locally Connected Spaces and Pseudo Locally Connected Spaces. Commentationes Mathematicae, Tome 50 (2010) no. 2. https://geodesic-test.mathdoc.fr/item/COMA_2010__50_2_291991/