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Locally compact linearly Lindelöf spaces

Kenneth Kunen (2002)

Commentationes Mathematicae Universitatis Carolinae

There is a locally compact Hausdorff space which is linearly Lindelöf and not Lindelöf. This answers a question of Arhangel'skii and Buzyakova.

Lonely points revisited

Jonathan L. Verner (2013)

Commentationes Mathematicae Universitatis Carolinae

In our previous paper, we introduced the notion of a lonely point, due to P. Simon. A point p X is lonely if it is a limit point of a countable dense-in-itself set, it is not a limit point of a countable discrete set and all countable sets whose limit point it is form a filter. We use the space 𝒢 ω from a paper of A. Dow, A.V. Gubbi and A. Szymański [Rigid Stone spaces within ZFC, Proc. Amer. Math. Soc. 102 (1988), no. 3, 745–748] to construct lonely points in ω * . This answers the question of P. Simon...

Longer chains of idempotents in βG

Neil Hindman, Dona Strauss, Yevhen Zelenyuk (2013)

Fundamenta Mathematicae

Given idempotents e and f in a semigroup, e ≤ f if and only if e = fe = ef. We show that if G is a countable discrete group, p is a right cancelable element of G* = βG∖G, and λ is a countable ordinal, then there is a strictly decreasing chain q σ σ < λ of idempotents in C p , the smallest compact subsemigroup of G* with p as a member. We also show that if S is any infinite subsemigroup of a countable group, then any nonminimal idempotent in S* is the largest element of such a strictly decreasing chain of idempotents....

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