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A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ

100%

Marciszewski W.

Fundamenta Mathematicae

1997

tom 153

nr 2

125-40

We construct two examples of infinite spaces X such that there is no continuous linear surjection from the space of continuous functions $c_p(X)$ onto $c_p(X)$ × ℝ$. In particular, $c_p(X)$ is not linearly homeomorphic to $c_p(X)$ × ℝ$. One of these examples is compact. This answers some questions of Arkhangel'skiĭ.

A contribution to the topological classification of the spaces Ср(X)

100%

Cauty R., Dobrowolski T., Marciszewski W.

Fundamenta Mathematicae

1993

tom 142

nr 3

269-301

We prove that for each countably infinite, regular space X such that $C_p(X)$ is a $Z_σ$-space, the topology of $C_p(X)$ is determined by the class $F_0(C_p(X))$ of spaces embeddable onto closed subsets of $C_p(X)$. We show that $C_p(X)$, whenever Borel, is of an exact multiplicative class; it is homeomorphic to the absorbing set $Ω_α$ for the multiplicative Borel class $M_α$ if $F_0(C_p(X)) = M_α$. For each ordinal α ≥ 2, we provide an example $X_α$ such that $C_p(X_α)$ is homeomorphic to $Ω_α$.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Marciszewski W.

1 Cauty R.

1 Dobrowolski T.

1 1997

1 1993

Wyniki wyszukiwania

A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ

A contribution to the topological classification of the spaces Ср(X)