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Volume 36, Issue 4
A Note on $Card(X)$

Weituo Dai, Meng Wang & Limin Sun

Anal. Theory Appl., 36 (2020), pp. 468-481.

Published online: 2020-12

[An open-access article; the PDF is free to any online user.]

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  • Abstract

The main interests here are to study the relationship between $card(X)$ and $card({\cal P}(X))$ and the connection between the separability of a space $X$ and cardinality of some function space on it. We will convert the calculation of  $card({\cal P}(X))$ to the calculation of $card({\cal F}(X\rightarrow Q))$.The main tool we used here is Zorn Lemma.

  • AMS Subject Headings

03E10

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COPYRIGHT: © Global Science Press

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@Article{ATA-36-468, author = {Dai , WeituoWang , Meng and Sun , Limin}, title = {A Note on $Card(X)$}, journal = {Analysis in Theory and Applications}, year = {2020}, volume = {36}, number = {4}, pages = {468--481}, abstract = {

The main interests here are to study the relationship between $card(X)$ and $card({\cal P}(X))$ and the connection between the separability of a space $X$ and cardinality of some function space on it. We will convert the calculation of  $card({\cal P}(X))$ to the calculation of $card({\cal F}(X\rightarrow Q))$.The main tool we used here is Zorn Lemma.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-SU4}, url = {http://global-sci.org/intro/article_detail/ata/18464.html} }
TY - JOUR T1 - A Note on $Card(X)$ AU - Dai , Weituo AU - Wang , Meng AU - Sun , Limin JO - Analysis in Theory and Applications VL - 4 SP - 468 EP - 481 PY - 2020 DA - 2020/12 SN - 36 DO - http://doi.org/10.4208/ata.OA-SU4 UR - https://global-sci.org/intro/article_detail/ata/18464.html KW - Cardinality, separability of space, Zorn Lemma. AB -

The main interests here are to study the relationship between $card(X)$ and $card({\cal P}(X))$ and the connection between the separability of a space $X$ and cardinality of some function space on it. We will convert the calculation of  $card({\cal P}(X))$ to the calculation of $card({\cal F}(X\rightarrow Q))$.The main tool we used here is Zorn Lemma.

Dai , WeituoWang , Meng and Sun , Limin. (2020). A Note on $Card(X)$. Analysis in Theory and Applications. 36 (4). 468-481. doi:10.4208/ata.OA-SU4
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