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Section
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Mathematics
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Title
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On projections of products of spaces
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Author(-s)
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Gryzlov A.A.a
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Affiliations
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Udmurt State Universitya
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Abstract
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We consider dense sets of products of topological spaces. We prove that in the product $Z^c=\prod\limits_{\alpha\in 2^\omega} Z_{\alpha},$ where $Z_\alpha=Z$ $(\alpha\in 2^\omega),$ there are dense sets such that their countable subsets have projections with additional properties. These properties entail that these dense sets contain no convergent sequences. By these properties we prove that the character of closed sets of the product is uncountable.
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Keywords
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product of spaces, projection, dense sets
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UDC
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54A25, 54B10
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MSC
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515.122
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DOI
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10.35634/vm210304
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Received
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25 July 2021
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Language
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Russian
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Citation
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Gryzlov A.A. On projections of products of spaces, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, issue 3, pp. 409-413.
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References
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