Precompact abelian groups and topological annihilators

For a compact Hausdorff abelian group K and its subgroup H, one defines the g-closure g(H) of H in K as the subgroup consisting of $\chi \in K$ such that $\chi(a_n)\longrightarrow 0$ in T=R/Z for every sequence {a_n} in $\hat K$ (the Pontryagin dual of K) that converges to 0 in the topology that H induces on $\hat K$. We prove that every countable subgroup of a compact Hausdorff group is g-closed, and thus give a positive answer to two problems of Dikranjan, Milan and Tonolo. We also show that every g-closed subgroup of a compact Hausdorff group is realcompact. The techniques developed in the paper are used to construct a close relative of the closure operator g that coincides with the $G_\delta$-closure on compact Hausdorff abelian groups, and thus captures realcompactness and pseudocompactness of subgroups.Comment: Version 1.0 - submitte

When a totally bounded group topology is the Bohr Topology of a LCA group

We look at the Bohr topology of maximally almost periodic groups (MAP, for short). Among other results, we investigate when a totally bounded abelian group $(G,w)$ is the Bohr reflection of a locally compact abelian group. Necessary and sufficient conditions are established in terms of the inner properties of $w$. As an application, an example of a MAP group $(G,t)$ is given such that every closed, metrizable subgroup $N$ of $bG$ with $N \cap G = \{0\}$ preserves compactness but $(G,t)$ does not strongly respects compactness. Thereby, we respond to Questions 4.1 and 4.3 in [comftrigwu]

Humility, Forgiveness, and Love -- The Heart of Ethical Stewardship

The purpose of this paper is to identify the nature and importance of ethical stewardship as a powerful contributor to the trustworthiness of leaders – focusing on humility, forgiveness, and love as three leadership qualities that are at the heart of ethical stewardship. We begin by defining ethical stewardship and equating it with Six characteristics of personal trustworthiness. Following that introduction, we explain why humility, forgiveness, and love are vitally important leadership qualities essential to becoming an effective ethical steward and include six propositions relating those three qualities to ethical stewardship. We then offer six insights about humility, forgiveness, and love that can assist those who wish to improve their ability to become ethical stewards to improve their success. We conclude the paper with a challenge to leaders to adopt ethical stewardship as their leadership paradigm

Exactly nn-resolvable Topological Expansions

For $\kappa$ a cardinal, a space X=(X,\sT) is $\kappa$-{\it resolvable} if $X$ admits $\kappa$-many pairwise disjoint \sT-dense subsets; (X,\sT) is {\it exactly} $\kappa$-{\it resolvable} if it is $\kappa$-resolvable but not $\kappa^+$-resolvable. The present paper complements and supplements the authors' earlier work, which showed for suitably restricted spaces (X,\sT) and cardinals $\kappa\geq\lambda\geq\omega$ that (X,\sT), if $\kappa$-resolvable, admits an expansion \sU\supseteq\sT, with (X,\sU) Tychonoff if (X,\sT) is Tychonoff, such that (X,\sU) is $\mu$-resolvable for all $\mu<\lambda$ but is not $\lambda$-resolvable (cf. Theorem~3.3 of \cite{comfhu10}). Here the "finite case" is addressed. The authors show in ZFC for $1<n<\omega$: (a) every $n$-resolvable space (X,\sT) admits an exactly $n$-resolvable expansion \sU\supseteq\sT; (b) in some cases, even with (X,\sT) Tychonoff, no choice of \sU is available such that (X,\sU) is quasi-regular; (c) if $n$-resolvable, (X,\sT) admits an exactly $n$-resolvable quasi-regular expansion \sU if and only if either (X,\sT) is itself exactly $n$-resolvable and quasi-regular or (X,\sT) has a subspace which is either $n$-resolvable and nowhere dense or is $(2n)$-resolvable. In particular, every $\omega$-resolvable quasi-regular space admits an exactly $n$-resolvable quasi-regular expansion. Further, for many familiar topological properties \PP, one may choose \sU so that (X,\sU)\in\PP if (X,\sT)\in\PP

Tychonoff Expansions with Prescribed Resolvability Properties

The recent literature offers examples, specific and hand-crafted, of Tychonoff spaces (in ZFC) which respond negatively to these questions, due respectively to Ceder and Pearson (1967) and to Comfort and Garc\'ia-Ferreira (2001): (1) Is every $\omega$-resolvable space maximally resolvable? (2) Is every maximally resolvable space extraresolvable? Now using the method of ${\mathcal{KID}}$ expansion, the authors show that {\it every} suitably restricted Tychonoff topological space (X,\sT) admits a larger Tychonoff topology (that is, an "expansion") witnessing such failure. Specifically the authors show in ZFC that if (X,\sT) is a maximally resolvable Tychonoff space with S(X,\sT)\leq\Delta(X,\sT)=\kappa, then (X,\sT) has Tychonoff expansions \sU=\sU_i ($1\leq i\leq5$), with \Delta(X,\sU_i)=\Delta(X,\sT) and S(X,\sU_i)\leq\Delta(X,\sU_i), such that (X,\sU_i) is: ($i=1$) $\omega$-resolvable but not maximally resolvable; ($i=2$) [if $\kappa'$ is regular, with S(X,\sT)\leq\kappa'\leq\kappa] $\tau$-resolvable for all $\tau<\kappa'$, but not $\kappa'$-resolvable; ($i=3$) maximally resolvable, but not extraresolvable; ($i=4$) extraresolvable, but not maximally resolvable; ($i=5$) maximally resolvable and extraresolvable, but not strongly extraresolvable.Comment: 25 pages, 0 figure

A Feminist Perspective on the Iraq War

In this article, the author historicizes her analysis of conditions for Iraqi women after the US invasion of 2003. Based on auto-biographical reflections, Al-Ali also presents her own trajectory as an academic-actvist and an activist-academic

Mother Mine: She Is Just Like You

https://digitalcommons.library.umaine.edu/mmb-vp/4893/thumbnail.jp

Correlational analysis between joint-level kinetics of countermovement jumps and weightlifting derivatives

The purpose of this study was to investigate the mechanical similarity between net joint moments (NJM) of the countermovement jump (CMJ) and the hang power clean (HPC) and jump shrug (JS). Twelve male Lacrosse players performed three maximal effort CMJs and three repetitions of the HPC and JS at 30%, 50%, and 70% of their HPC one repetition maximum (1-RM). Ground reaction forces and motion capture data were used to calculate the NJM of the hip, knee, and ankle joints during each exercise. Statistical comparison of the peak NJM indicated that NJM during the HPC and JS across all loads were equal to or greater than the NJM during the CMJ (all p < 0.025). In addition, correlation analyses indicated that CMJ hip NJM were associated (all p < 0.025) with HPC hip NJM at 30% and 70% (r = 0.611-0.822) and JS hip NJM at 50% and 70% (r = 0.674-0.739), whereas CMJ knee NJM were associated with HPC knee NJM at 70% (r = 0.638) and JS knee NJM at 50% and 70% (r = 0.664-0.732). Further, CMJ ankle NJM were associated with HPC ankle NJM at 30% and 50% (r = 0.615-0.697) and JS ankle NJM at 30%, 50%, and 70% (r = 0.735-0.824). Lastly, knee and ankle NJM during the JS were greater than during the HPC at 30% and 50% of 1-RM (all p < 0.017). The degree of mechanical similarity between the CMJ and the HPC and JS is dependent on the respective load and joint. [Abstract copyright: © Journal of Sports Science and Medicine.