Some non-multiplicative properties are l -invariant

Vladimir Vladimirovich Tkachuk

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 1, page 169-175
  • ISSN: 0010-2628

Abstract

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A cardinal function ϕ (or a property 𝒫 ) is called l -invariant if for any Tychonoff spaces X and Y with C p ( X ) and C p ( Y ) linearly homeomorphic we have ϕ ( X ) = ϕ ( Y ) (or the space X has 𝒫 ( ≡ X ⊢ 𝒫 ) iff Y ⊢ 𝒫 ). We prove that the hereditary Lindelöf number is l -invariant as well as that there are models of Z F C in which hereditary separability is l -invariant.

How to cite

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Tkachuk, Vladimir Vladimirovich. "Some non-multiplicative properties are $l$-invariant." Commentationes Mathematicae Universitatis Carolinae 38.1 (1997): 169-175. <http://eudml.org/doc/248062>.

@article{Tkachuk1997,
abstract = {A cardinal function $\varphi $ (or a property $\mathcal \{P\}$) is called $l$-invariant if for any Tychonoff spaces $X$ and $Y$ with $C_p(X)$ and $C_p(Y)$ linearly homeomorphic we have $\varphi (X)=\varphi (Y)$ (or the space $X$ has $\mathcal \{P\}$ ($\equiv X\vdash \{\mathcal \{P\}\}$) iff $Y\vdash \mathcal \{P\}$). We prove that the hereditary Lindelöf number is $l$-invariant as well as that there are models of $ZFC$ in which hereditary separability is $l$-invariant.},
author = {Tkachuk, Vladimir Vladimirovich},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$l$-equivalent spaces; $l$-invariant property; hereditary Lindelöf number; -equivalent spaces; -invariant property; hereditary Lindelöf number},
language = {eng},
number = {1},
pages = {169-175},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some non-multiplicative properties are $l$-invariant},
url = {http://eudml.org/doc/248062},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Tkachuk, Vladimir Vladimirovich
TI - Some non-multiplicative properties are $l$-invariant
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 1
SP - 169
EP - 175
AB - A cardinal function $\varphi $ (or a property $\mathcal {P}$) is called $l$-invariant if for any Tychonoff spaces $X$ and $Y$ with $C_p(X)$ and $C_p(Y)$ linearly homeomorphic we have $\varphi (X)=\varphi (Y)$ (or the space $X$ has $\mathcal {P}$ ($\equiv X\vdash {\mathcal {P}}$) iff $Y\vdash \mathcal {P}$). We prove that the hereditary Lindelöf number is $l$-invariant as well as that there are models of $ZFC$ in which hereditary separability is $l$-invariant.
LA - eng
KW - $l$-equivalent spaces; $l$-invariant property; hereditary Lindelöf number; -equivalent spaces; -invariant property; hereditary Lindelöf number
UR - http://eudml.org/doc/248062
ER -

References

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  6. Engelking R., General Topology, PWN, Warszawa, 1977. Zbl0684.54001MR0500780
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  9. Tkachuk V.V., On a method of constructing examples of M -equivalent spaces (in Russian), Uspehi Mat. Nauk 38 6 (1983), 127-128. (1983) MR0728737
  10. Todorčević S., Forcing positive partition relations, Trans. Amer. Math. Soc. 280 2 (1983), 703-720. (1983) MR0716846

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