Ai-maximal independent families and irresolvable Baire spaces
نویسندگان
چکیده
منابع مشابه
Strongly irresolvable spaces
Several new characterizations of strongly irresolvable topological spaces are found and precise relationships are noted between strong irresolvability, hereditary irresolvability, and submaximality. It is noted that strong irresolvablity is a faint topological property, while neither hereditary irresolvablity nor submaximality are semitopological.
متن کاملBaire Spaces, Sober Spaces
In the article concepts and facts necessary to continue forma-lization of theory of continuous lattices according to [10] are introduced. The notation and terminology used here are introduced in the following papers:
متن کاملMaximal independent families and a topological consequence
For κ ω and X a set, a familyA⊆P(X) is said to be κ-independent on X if |⋂A∈F Af (A)| κ for each F ∈ [A]<ω and f ∈ {−1,+1}F ; here A+1 =A and A−1 =X\A. Theorem 3.6. For κ ω, some A ⊆ P(κ) with |A| = 2κ is simultaneously maximal κindependent and maximal ω-independent on κ . The family A may be chosen so that every two elements of κ are separated by 2κ -many elements of A. Corollary 5.4. For κ ω ...
متن کاملScattered, Hausdorff-reducible, and hereditarily irresolvable spaces
We show that a topological space is hereditarily irresolvable if and only if it is Hausdorff-reducible. We construct a compact irreducible T1-space and a connected Hausdorff space, each of which is strongly irresolvable. Furthermore, we show that the three notions of scattered, Hausdorff-reducible, and hereditarily irresolvable coincide for a large class of spaces, including metric, locally com...
متن کاملA note on Volterra and Baire spaces
In Proposition 2.6 in (G. Gruenhage, A. Lutzer, Baire and Volterra spaces, textit{Proc. Amer. Math. Soc.} {128} (2000), no. 10, 3115--3124) a condition that every point of $D$ is $G_delta$ in $X$ was overlooked. So we proved some conditions by which a Baire space is equivalent to a Volterra space. In this note we show that if $X$ is a monotonically normal $T_1...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2014
ISSN: 0166-8641
DOI: 10.1016/j.topol.2014.06.007