TY - JOUR T1 - Cardinalities of Restricted Ranges 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.