Geodesic
Local $\tau$-density of the sum and the superextension of topological spaces
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations, geometry, and topology, Tome 201 (2021), pp. 103-106

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In this paper, we study the density and the local density of the superextension of topological spaces. We prove that if $X_{\alpha}$ is a locally $\tau$-dense space for each $\alpha\in A$, then $X=\bigoplus \{X_{\alpha}: \alpha\in A\}$ is also a locally $\tau$-dense space. We also prove that for any infinite $T_{1}$-space, the inequality $ld(\lambda_{c}X)\le ld(X) $ is always valid.
Keywords: topological space, local density, separability, superextension, cardinal number. 
@article{INTO_2021_201_a8,
     author = {F. G. Mukhamadiev},
     title = {Local $\tau$-density of the sum and the superextension of topological spaces},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {103--106},
     publisher = {mathdoc},
     volume = {201},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_201_a8/}
}
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F. G. Mukhamadiev. Local $\tau$-density of the sum and the superextension of topological spaces. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations, geometry, and topology, Tome 201 (2021), pp. 103-106. http://geodesic.mathdoc.fr/item/INTO_2021_201_a8/