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

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

Published online: 2020-12

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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.

• Keywords

Cardinality, separability of space, Zorn Lemma.

03E10

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@Article{ATA-36-468, author = {Weituo and Dai and and 9749 and and Weituo Dai and Meng and Wang and and 9750 and and Meng Wang and Limin and Sun and and 9751 and and Limin Sun}, 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.

Weituo Dai, Meng Wang & Limin Sun. (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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