pseudocompact

English

Etymology

pseudo- +‎ compact

Adjective

pseudocompact (not comparable)

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

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