Productivity of sequences with respect to a given weight function

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F44555601%3A13440%2F11%3A43880170" target="_blank" >RIV/44555601:13440/11:43880170 - isvavai.cz</a>
Result on the web
<a href="http://pdn.sciencedirect.com/science?_ob=MiamiImageURL&_cid=271523&_user=640945&_pii=S0166864110003615&_check=y&_origin=article&_zone=toolbar&_coverDate=15-Feb-2011&view=c&origi" target="_blank" >http://pdn.sciencedirect.com/science?_ob=MiamiImageURL&_cid=271523&_user=640945&_pii=S0166864110003615&_check=y&_origin=article&_zone=toolbar&_coverDate=15-Feb-2011&view=c&origi</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
Productivity of sequences with respect to a given weight function
Original language description
Given a function $f:Nto(omega+1)setminus{0}$, we say that a faithfully indexed sequence ${a_n:ninN}$ of elements of a topological group $G$ is: (i)~{em $f$-Cauchy productive ($f$-productive)/} provided that the sequence ${prod_{n=0}^m a_n^{z(n)}:minN}$ is left Cauchy (converges to some element of $G$, respectively) for each function $z:NtoZ$ such that $|z(n)|le f(n)$ for every $ninN$; (ii)~{em unconditionally $f$-Cauchy productive (unconditionally $f$-productive)/} provided thatthe sequence ${a_{varphi(n)}:ninN}$ is $(fcircvarphi)$-Cauchy productive (respectively, $(fcircvarphi)$-productive) for every bijection $varphi:NtoN$. (Bijections can be replaced by injections here.) We consider the question of existence of(unconditionally) $f$-productive sequences for a given ``weight function'' $f$. We prove that: (1) a Hausdorff group having an $f$-productive sequence for some $f$ contains a homeomorphic copy of the Cantor set; (2) if a non-discrete gro
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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