اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the cardinality of Extremally Disconnected Groups with Linear Topology
71
0
0.0
(
0
)
تأليف
Olga Sipacheva
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A group topology is said to be linear if open subgroups form a base of neighborhoods of the identity element. It is proved that the existence of a nondiscrete extremally disconnected group of Ulam nonmeasurable cardinality with linear topology implies that of a nondiscrete extremally disconnected group of cardinality at most $2^omega$ with linear topology.
قيم البحث
اقرأ أيضاً
Given an arbitrary measurable cardinal $kappa$, a nondiscrete Hausdorff extremally disconnected topological group of cardinality $kappa$ is constructed.
It is proved that the existence of a countable extremally disconnected Boolean topological group containing a family of open subgroups whose intersection has empty interior implies the existence of a rapid ultrafilter.
It is proved that any countable topological group in which the filter of neighborhoods of the identity element is not rapid contains a discrete set with precisely one nonisolated point. This gives a negative answer to Protasovs question on the existe
nce in ZFC of a countable nondiscrete group in which all discrete subsets are closed. It is also proved that the existence of a countable nondiscrete extremally disconnected group implies the existence of a rapid ultrafilter and, hence, a countable nondiscrete extremally disconnected group cannot be constructed in ZFC.
Elementary band representations are the fundamental building blocks of atomic limit band structures. They have the defining property that at partial filling they cannot be both gapped and trivial. Here, we give two examples -- one each in a symmorphi
c and a non-symmorphic space group -- of elementary band representations realized with an energy gap. In doing so, we explicitly construct a counterexample to a claim by Michel and Zak that single-valued elementary band representations in non-symmorphic space groups with time-reversal symmetry are connected. For each example, we construct a topological invariant to explicitly demonstrate that the valence bands are non-trivial. We discover a new topological invariant: a movable but unremovable Dirac cone in the Wilson Hamiltonian and a bent-Z2 index.
For a Tychonoff space $X$ and a subspace $Ysubsetmathbb R$, we study Baire category properties of the space $C_{downarrow F}(X,Y)$ of continuous functions from $X$ to $Y$, endowed with the Fell hypograph topology. We characterize pairs $X,Y$ for whic
h the function space $C_{downarrow F}(X,Y)$ is $infty$-meager, meager, Baire, Choquet, strong Choquet, (almost) complete-metrizable or (almost) Polish.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
