Between local connectedness and sum connectedness

J.K. Kohli, D. Singh, and B.K. Tyagi. "Between local connectedness and sum connectedness." Commentationes Mathematicae 53.1 (2013): null. <http://eudml.org/doc/291465>.

@article{J2013,
abstract = {A new generalization of local connectedness called Z-local connectedness is introduced. Basic properties of Z-locally connected spaces are studied and their place in the hierarchy of variants of local connectedness, which already exist in the literature, is elaborated. The class of Z-locally connected spaces lies strictly between the classes of pseudo locally connected spaces (Commentations Math. 50(2)(2010),183-199) and sum connected spaces ($\equiv $ weakly locally connected spaces) (Math. Nachrichten 82(1978), 121-129; Ann. Acad. Sci. Fenn. AI Math. 3(1977), 185-205) and so contains all quasi locally connected spaces which in their turn contain all almost locally connected spaces introduced by Mancuso (J. Austral. Math. Soc. 31(1981), 421-428). Formulations of product and subspace theorems for Z-locally connected spaces are suggested. Their preservation under mappings and their interplay with mappings are discussed. Change of topology of a Z-locally connected space is considered so that it is simply a locally connected space in the coarser topology. It turns out that the full subcategory of Z-locally connected spaces provides another example of a mono-coreflective subcategory of TOP which properly contains all almost locally connected spaces.},
author = {J.K. Kohli, D. Singh, B.K. Tyagi},
journal = {Commentationes Mathematicae},
keywords = {Z-locally connected space, almost (quasi, pseudo) locally connected space, sum connected space, regular open set, regular $F_\sigma $-set, $\theta $-open set, cl-supercontinuous function, mono-coreflective subcategory},
language = {eng},
number = {1},
pages = {null},
title = {Between local connectedness and sum connectedness},
url = {http://eudml.org/doc/291465},
volume = {53},
year = {2013},
}

TY - JOUR
AU - J.K. Kohli
AU - D. Singh
AU - B.K. Tyagi
TI - Between local connectedness and sum connectedness
JO - Commentationes Mathematicae
PY - 2013
VL - 53
IS - 1
SP - null
AB - A new generalization of local connectedness called Z-local connectedness is introduced. Basic properties of Z-locally connected spaces are studied and their place in the hierarchy of variants of local connectedness, which already exist in the literature, is elaborated. The class of Z-locally connected spaces lies strictly between the classes of pseudo locally connected spaces (Commentations Math. 50(2)(2010),183-199) and sum connected spaces ($\equiv $ weakly locally connected spaces) (Math. Nachrichten 82(1978), 121-129; Ann. Acad. Sci. Fenn. AI Math. 3(1977), 185-205) and so contains all quasi locally connected spaces which in their turn contain all almost locally connected spaces introduced by Mancuso (J. Austral. Math. Soc. 31(1981), 421-428). Formulations of product and subspace theorems for Z-locally connected spaces are suggested. Their preservation under mappings and their interplay with mappings are discussed. Change of topology of a Z-locally connected space is considered so that it is simply a locally connected space in the coarser topology. It turns out that the full subcategory of Z-locally connected spaces provides another example of a mono-coreflective subcategory of TOP which properly contains all almost locally connected spaces.
LA - eng
KW - Z-locally connected space, almost (quasi, pseudo) locally connected space, sum connected space, regular open set, regular $F_\sigma $-set, $\theta $-open set, cl-supercontinuous function, mono-coreflective subcategory
UR - http://eudml.org/doc/291465
ER -