Small uncountable powers of the Sorgenfrey line may not be weakly pseudocompact
Keywords:
Sorgenfrey, pseudocompact, product spacesAbstract
It is established that if Martin's Axiom $M A(\kappa)$ holds for some cardinal $\kappa$, then the $\kappa$-power $\mathbb{S}^\kappa$, of the Sorgenfrey line $\mathbb{S}$, is not weakly pseudocompact.
References
A. Arhangel'skii and M. Tkachenko, Topological Groups and Related Structures. Atlantis Studies in Mathematics, vol. 1. Paris-Amsterdam: Atlantis Press/World Scientific, 2008.
A. Dorantes-Aldama, O. Okunev, Á. Tamariz-Mascarúa, Weakly pseudocompact spaces, in Pseudocompact Topological Spaces. Eds. M. Hrǔsák, Á. TamarizMascarúa, M. Tkachenko. Springer, Cham, 2018, 75-102.
F. W. Eckertson, Sums, products, and mappings of weakly pseudocompact spaces, Topology Appl. 72 (1996), no. 2, 149-157.
F. Hernández-Hernández, R. Rojas-Hernńdez, Á. Tamariz-Mascarúa, Non-trivial non weakly pseudocompact spaces, Topology Appl. 247 (2018), 1-8.
S. García-Ferreira and A. García-Máynez, On weakly-pseudocompact spaces, Houston J. Math. 20 (1994), no. 1, 145-159.
E. Hewitt, Rings of real-valued continuous functions I, Trans. Amer. Math. Soc. 64 (1948), 45-99.
