# Property C'', strong measure zero sets and subsets of the plane

Fundamenta Mathematicae (1997)

- Volume: 153, Issue: 3, page 277-293
- ISSN: 0016-2736

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topPawlikowski, Janusz. "Property C'', strong measure zero sets and subsets of the plane." Fundamenta Mathematicae 153.3 (1997): 277-293. <http://eudml.org/doc/212224>.

@article{Pawlikowski1997,

abstract = {Let X be a set of reals. We show that
• X has property C" of Rothberger iff for all closed F ⊆ ℝ × ℝ with vertical sections $F_x$ (x ∈ X) null, $∪_\{x ∈ X\}F_x$ is null;
• X has strong measure zero iff for all closed F ⊆ ℝ × ℝ with all vertical sections $F_x$ (x ∈ ℝ) null, $∪_\{x ∈ X\}F_x$ is null.},

author = {Pawlikowski, Janusz},

journal = {Fundamenta Mathematicae},

keywords = {Rothberger property; strong measure zero},

language = {eng},

number = {3},

pages = {277-293},

title = {Property C'', strong measure zero sets and subsets of the plane},

url = {http://eudml.org/doc/212224},

volume = {153},

year = {1997},

}

TY - JOUR

AU - Pawlikowski, Janusz

TI - Property C'', strong measure zero sets and subsets of the plane

JO - Fundamenta Mathematicae

PY - 1997

VL - 153

IS - 3

SP - 277

EP - 293

AB - Let X be a set of reals. We show that
• X has property C" of Rothberger iff for all closed F ⊆ ℝ × ℝ with vertical sections $F_x$ (x ∈ X) null, $∪_{x ∈ X}F_x$ is null;
• X has strong measure zero iff for all closed F ⊆ ℝ × ℝ with all vertical sections $F_x$ (x ∈ ℝ) null, $∪_{x ∈ X}F_x$ is null.

LA - eng

KW - Rothberger property; strong measure zero

UR - http://eudml.org/doc/212224

ER -

## References

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