On regular separable countably compact \(\mathbb{R}\)-rigid spaces. (English) Zbl 1523.54009
A topological space \(X\) is called \(\mathbb R\)-rigid if every continuous real-valued function on \(X\) is constant. Tzannes asked if there is a regular separable countably compact \(\mathbb R\)-rigid space. The authors give an affirmative answer to this question. Further, they prove that it is consistent that there is a regular separable first countable countably compact \(\mathbb R\)-rigid space. The authors construct a regular separable sequentially compact space which is not Tychonoff, answering a question of Banakh, Bardyla, and Ravsky [T. Banakh et al., Topology Appl. 280, Article ID 107277, 11 p. (2020; Zbl 1448.54013)].
Reviewer: Akira Iwasa (Big Spring)
MSC:
| 54A35 | Consistency and independence results in general topology |
| 03E35 | Consistency and independence results |
Citations:
Zbl 1448.54013Software:
MathOverflowReferences:
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