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Volume 2, Issue 1
Cardinalities of Restricted Ranges

Ying-Guang Shi

J. Comp. Math., 2 (1984), pp. 33-40.

Published online: 1984-02

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  • Abstract

Let $l$ and $u$ be upper and lower semicontinuous extended functions on [a,b], respectively, with $l≤u$. Let $H$ be an n-dimensional Haar subspace and $K=\{p\in H:l\leq p\leq u\}$. This paper gives complete characterizations of K satisfying $$card \ K=0 \ or \ 1 \  or \ ∞$$ under certain assumptions, where card K denotes the cardinality of K.

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@Article{JCM-2-33, author = {Ying-Guang Shi}, title = {Cardinalities of Restricted Ranges}, journal = {Journal of Computational Mathematics}, year = {1984}, volume = {2}, number = {1}, pages = {33--40}, abstract = {

Let $l$ and $u$ be upper and lower semicontinuous extended functions on [a,b], respectively, with $l≤u$. Let $H$ be an n-dimensional Haar subspace and $K=\{p\in H:l\leq p\leq u\}$. This paper gives complete characterizations of K satisfying $$card \ K=0 \ or \ 1 \  or \ ∞$$ under certain assumptions, where card K denotes the cardinality of K.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9637.html} }
TY - JOUR T1 - Cardinalities of Restricted Ranges AU - Ying-Guang Shi JO - Journal of Computational Mathematics VL - 1 SP - 33 EP - 40 PY - 1984 DA - 1984/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9637.html KW - AB -

Let $l$ and $u$ be upper and lower semicontinuous extended functions on [a,b], respectively, with $l≤u$. Let $H$ be an n-dimensional Haar subspace and $K=\{p\in H:l\leq p\leq u\}$. This paper gives complete characterizations of K satisfying $$card \ K=0 \ or \ 1 \  or \ ∞$$ under certain assumptions, where card K denotes the cardinality of K.

Ying-Guang Shi. (1984). Cardinalities of Restricted Ranges. Journal of Computational Mathematics. 2 (1). 33-40. doi:
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