isometries of spaces of radon measures
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2017
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Abstract
Let Ω and I denote a compact metrizable space with card(Ω)≥2 and the unit interval, respectively. We prove Milutin and Cantor-Bernstein type theorems for the spaces M(Ω) of Radon measures on compact Hausdorff spaces Ω. In particular, we obtain the following results: (1) for every infinite closed subset K of βN the spaces M(K), M(βN), and M(Ω2ℵ0) are order-isometric; (2) for every discrete space Γ with m≔card(Γ)>ℵ0 the spaces M(βΓ) and M(I2m) are order-isometric, whereas there is no linear homeomorphic injection from C(βT) into C(I2m).
| Reference Key |
wjtowicz2017journalisometries
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|---|---|
| Authors | ;Marek Wójtowicz |
| Journal | Biosensors |
| Year | 2017 |
| DOI |
10.1155/2017/3850817
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