Geodesic
Some topological and cardinal properties of the space of permutation degree
Filomat, Tome 36 (2022) no. 20, p. 7059

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DOI

In this paper, we prove a few facts and some cardinal properties of the space of permutation degree introduced in [6]. More precisely, we prove that if the product X n is a Lindelöf (resp. locally Lindelöf) space, then the space SP n X is also Lindelöf (resp. locally Lindelöf). We also prove that if the product X n is a weakly Lindelöf (resp. weakly locally Lindelöf) space, then the space SP n X is also weakly Lindelöf (resp. weakly locally Lindelöf). Moreover, we investigate the preservation of the network weight, π-character and local density of topological spaces by the functor of G-permutation degree. It is proved that this functor preserves the network weight, π-character and local density of infinite topological T 1-spaces.
DOI : 10.2298/FIL2220059K
Classification : 54B30, 18A05, 18F60, 54A25
Keywords: Lindelöf, almost Lindelöf, weakly Lindelöf quasi-Lindelöf, τ-placed, network weight, π-character 
Ljubiša D R Kočinac; Farkhod G Mukhamadiev; Anvar K Sadullaev. Some topological and cardinal properties of the space of permutation degree. Filomat, Tome 36 (2022) no. 20, p. 7059 . doi: 10.2298/FIL2220059K
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     title = {Some topological and cardinal properties of the space of permutation degree},
     journal = {Filomat},
     pages = {7059 },
     year = {2022},
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     number = {20},
     doi = {10.2298/FIL2220059K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2220059K/}
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