Cardinal invariants of coset spaces

Abstract A topological space X is called a coset space if X is homeomorphic to a quotient space G / H of left cosets, for some closed subgroup H of a topological group G. In this paper, we investigate the cardinal invariants of coset spaces. We first show that if H is a closed neutral subgroup of a topological group G, then △ ( G / H ) = ψ ( G / H ) , w ( G / H ) = d ( G / H ) ⋅ χ ( G / H ) and w ( G / H ) = l ( G / H ) ⋅ χ ( G / H ) . We also prove that if H is a closed subgroup of a feathered topological group G, then (1) w ( G / H ) = d ( G / H ) ⋅ χ ( G / H ) and w ( G / H ) = l ( G / H ) ⋅ χ ( G / H ) ; (2) the quotient space G / H is metrizable if and only if G / H is first-countable. At the end, we consider some applications of sp-networks in coset spaces. In particular, we show that if H is a closed neutral subgroup of a topological group G, then (1) s p n w ( G / H ) = d ( G / H ) ⋅ s p χ ( G / H ) ; (2) the quotient space G / H is metrizable if and only if G / H has countable sp-character.