pseudocompact

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 ${\\displaystyle \\lambda ^{0}}$-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..