pseudocompact

From pseudo- +‎ compact.

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pseudocompact space

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pseudocompact (not comparable)

1. (mathematics, of a space) having a bounded image
   • 2015, Oleg Gutik, Oleksandr Ravsky, “Pseudocompactness, products and topological Brandt ${\displaystyle \lambda ^{0}}$-extensions of semitopological monoids”, in arXiv‎:

     In particular we show that if ${\displaystyle {\big \{}{\big (}B_{\lambda _{i}}^{0}(S_{i}),\tau _{B(S_{i})}^{0}{\big )}\colon i\in {\mathcal {I}}{\big \}}}$ is a family of Hausdorff pseudocompact to\-pological Brandt ${\displaystyle \lambda _{i}^{0}}$-extensions of pseudocompact semitopological monoids with zero such that the Tychonoff product ${\displaystyle \prod \left\{S_{i}\colon i\in {\mathcal {I}}\right\}}$ is a pseudocompact space then the direct product ${\displaystyle \prod {\big \{}{\big (}B_{\lambda _{i}}^{0}(S_{i}),\tau _{B(S_{i})}^{0}{\big )}\colon i\in {\mathcal {I}}{\big \}}}$ endowed with the Tychonoff topology is a Hausdorff pseudocompact semitopological semigroup..