Finite-valued mappings preserving dimension

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F44555601%3A13440%2F11%3A43880563" target="_blank" >RIV/44555601:13440/11:43880563 - isvavai.cz</a>
Result on the web
<a href="https://mynsmstore.uh.edu/index.php?route=product/product&product_id=26408" target="_blank" >https://mynsmstore.uh.edu/index.php?route=product/product&product_id=26408</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.topol.2010.11.009" target="_blank" >10.1016/j.topol.2010.11.009</a>

Result language
angličtina
Original language name
Finite-valued mappings preserving dimension
Original language description
We say that a set-valued mapping $F:XRightarrow Y$ is {em sig{C}} provided that there exists a countable cover $mathcal{C}$ of $X$ consisting of functionally closed sets such that for every $Cinmathcal{C}$ and each functionally open set $Usubset Y$ one can find a functionally open set $Vsubset X$ such that ${xin C:F(x)cap Uneqemptyset}=Ccap V$. For Tychonoff spaces $X$ and $Y$ we write $Xvartriangleright Y$ provided that there exist a finite-valued sig{C} mapping $F:XRightarrow Y$ anda finite-valued sig{D} mapping $G:YRightarrow X$ (for suitable $mathcal{C}$ and $mathcal{D}$) such that $yin bigcup{F(x):xin G(y)}$ for every $yin Y$. We prove that $Xvartriangleright Y$ implies $dim Xgeqdim Y$. (Here $dim X$ denotes thev{C}ech-Lebesgue (covering) dimension of $X$.) As a corollary, we obtain that $dim X=dim Y$ whenever a perfectly normal space $Y$ is an image of a Tychonoff space $X$ under a finite-to-one open mapping. We also give an example of an o
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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