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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  1. Arhangel'skii A.V., Structure and classification of topological spaces and cardinal invariants (in Russian), Uspehi Mat. Nauk 33 6 (1978), 29-84. (1978) MR0526012
  2. Arhangel'skii A.V., On relationship between the invariants of topological groups and their subspaces (in Russian), Uspehi Mat. Nauk 35 3 (1980), 3-22. (1980) MR0580615
  3. Arhangel'skii A.V., Topological function spaces (in Russian), Moscow University Publishing House, Moscow, 1989. MR1017630
  4. Arhangel'skii A.V., C p -theory, in: Recent Progress in General Topology, edited by J. van Mill and M. Hušek, North Holland, 1992, pp.1-56. Zbl0932.54015MR1229121
  5. Arhangel'skii A.V., Ponomarev V.I., General Topology in Problems and Exercises (in Russian), Nauka Publishing House, Moscow, 1974. MR0239550
  6. Engelking R., General Topology, PWN, Warszawa, 1977. Zbl0684.54001MR0500780
  7. Gul'ko S.P., Khmyleva T.E., The compactness is not preserved by t -equivalence (in Russian), Mat. Zametki 39 6 (1986), 895-903. (1986) MR0855937
  8. Pestov V.G., Some topological properties are preserved by M -equivalence (in Russian), Uspehi Mat. Nauk 39 6 (1984), 203-204. (1984) MR0771108
  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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