## The weight and $$i$$-weight of Lindelöf $$P$$-groups.(English)Zbl 1535.22003

Let $$X$$ be a $$P$$-space. Recall that a Tychonoff space $$X$$ is called a $$P$$-space if every $$G_\delta$$-set in $$X$$ is open. In this article, the author shows:
(1)
The pseudo-$$\aleph_1$$-compactness of $$X$$ is equivalent to the pseudo-$$\aleph_1$$-compactness of the free topological group $$F(X)$$ over $$X$$.
(2)
$$X$$ is $$\aleph_1$$-stable.
(3)
If in addition $$X$$ is Lindelöf, the exact value of the weight of $$F(X)$$ is calculated.
(4)
If in addition $$X$$ is a Lindelöf group, a nontrivial relationship between the weight and $$i$$-weight is presented.

### MSC:

 22A05 Structure of general topological groups 54H11 Topological groups (topological aspects) 54D30 Compactness 54G20 Counterexamples in general topology
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### References:

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