Coset spaces and cardinal invariants

Fernández, Manuel García; Sánchez, Iván; Tkachenko, Mikhail

doi:10.1007/s10474-019-00959-w

Cited by 17 publications

(1 citation statement)

References 10 publications

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“…Example 3.5. [25] The two arrows space is a compact coset space which is first-countable, but not submetrizable.…”

Section: Preliminarymentioning

confidence: 99%

Quotient spaces with strong subgyrogroups

Meng¹,

Ling²,

Xu³

2022

Preprint

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In this paper, we mainly investigate the quotient spaces G/H when G is a strongly topological gyrogroup and H is a strong subgyrogroup of G. It is shown that if G is a strongly topological gyrogroup, H is a closed strong subgyrogroup of G and H is inner neutral, then the quotient space G/H is first-countable if and only if G/H is a bisequential space if and only if G/H is a weakly first-countable space if and only if G/H is a csf -countable and sequential α 7 -space. Moreover, it is shown that if G is a strongly topological gyrogroup and H is a locally compact strong subgyrogroup of G, then there exists an open neighborhood U of the identity element 0 such that π(U ) is closed in G/H and the restriction of π to U is a perfect mapping from U onto the subspace π(U ); if H is a locally compact metrizable strong subgyrogroup of G and the quotient space G/H is sequential, then G is also sequential; if H is a closed first-countable and separable strong subgyrogroup of G, the quotient space G/H is an ℵ 0 -space, then G is an ℵ 0 -space; if the quotient space G/H is a cosmic space, then G is also a cosmic space; if the quotient space G/H has a star-countable cs-network or star-countable wcs * -network, then G also has a star-countable cs-network or star-countable wcs * -network, respectively.

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“…Example 3.5. [25] The two arrows space is a compact coset space which is first-countable, but not submetrizable.…”

Section: Preliminarymentioning

confidence: 99%