# Extending real-valued functions in βκ

Fundamenta Mathematicae (1997)

- Volume: 152, Issue: 1, page 21-41
- ISSN: 0016-2736

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topDow, Alan. "Extending real-valued functions in βκ." Fundamenta Mathematicae 152.1 (1997): 21-41. <http://eudml.org/doc/212197>.

@article{Dow1997,

abstract = {An Open Coloring Axiom type principle is formulated for uncountable cardinals and is shown to be a consequence of the Proper Forcing Axiom. Several applications are found. We also study dense C*-embedded subspaces of ω*, showing that there can be such sets of cardinality $c$ and that it is consistent that ω*\{pis C*-embedded for some but not all p ∈ ω*.
},

author = {Dow, Alan},

journal = {Fundamenta Mathematicae},

keywords = {Proper Forcing Axiom; Open Colouring Axiom; -embedding; Čech-Stone compactification; first-countability; countable separability; reflection theorem for ideals of countable sets; Hausdorff-Luzin-type gap; finite-to-one graph type family; countably tight space; Martin's Axiom},

language = {eng},

number = {1},

pages = {21-41},

title = {Extending real-valued functions in βκ},

url = {http://eudml.org/doc/212197},

volume = {152},

year = {1997},

}

TY - JOUR

AU - Dow, Alan

TI - Extending real-valued functions in βκ

JO - Fundamenta Mathematicae

PY - 1997

VL - 152

IS - 1

SP - 21

EP - 41

AB - An Open Coloring Axiom type principle is formulated for uncountable cardinals and is shown to be a consequence of the Proper Forcing Axiom. Several applications are found. We also study dense C*-embedded subspaces of ω*, showing that there can be such sets of cardinality $c$ and that it is consistent that ω*{pis C*-embedded for some but not all p ∈ ω*.

LA - eng

KW - Proper Forcing Axiom; Open Colouring Axiom; -embedding; Čech-Stone compactification; first-countability; countable separability; reflection theorem for ideals of countable sets; Hausdorff-Luzin-type gap; finite-to-one graph type family; countably tight space; Martin's Axiom

UR - http://eudml.org/doc/212197

ER -

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