Connectedness and local connectedness of topological groups and extensions

summary:It is shown that both the free topological group $F(X)$ and the free Abelian topological group $A(X)$ on a connected locally connected space $X$ are locally connected. For the Graev's modification of the groups $F(X)$ and $A(X)$, the corresponding result is more symmetric: the groups $F\Gamma(X)$ and $A\Gamma(X)$ are connected and locally connected if $X$ is. However, the free (Abelian) totally bounded group $FTB(X)$ (resp., $ATB(X)$) is not locally connected no matter how ``good'' a space $X$ is. The above results imply that every non-trivial continuous homomorphism of $A(X)$ to the additive group of reals, with $X$ connected and locally connected, is open. We also prove that any dense in itself subspace of the Sorgenfrey line has a Urysohn connectification. If $D$ is a dense subset of $\{0,1\}^{\frak c}$ of power less than $\frak c$, then $D$ has a Urysohn connectification of the same cardinality as $D$. We also strengthen a result of [1] for second countable Tychonoff spaces without open compact subspaces proving that it is possible to find a compact metrizable connectification of such a space preserving its dimension if it is positive

Empty spaces and the value of symbols: Estonia's 'war of monuments' from another angle

Taking as its point of departure the recent heightened discussion surrounding publicly sited monuments in Estonia, this article investigates the issue from the perspective of the country's eastern border city of Narva, focusing especially upon the restoration in 2000 of a 'Swedish Lion' monument to mark the 300th anniversary of Sweden's victory over Russia at the first Battle of Narva. This commemoration is characterised here as a successful local negotiation of a potentially divisive past, as are subsequent commemorations of the Russian conquest of Narva in 1704. A recent proposal to erect a statue of Peter the Great in the city, however, briefly threatened to open a new front in Estonia's ongoing 'war of monuments'. Through a discussion of these episodes, the article seeks to link the Narva case to broader conceptual issues of identity politics, nationalism and post-communist transition

When is |C(X x Y)| = |C(X)||C(Y)|?

Sufficient conditions on the Tychonoff spaces X and Y are found that imply that the equation in the title holds. Sufficient conditions on the Tychonoff space X are found that ensure that the equation holds for every Tychonoff space Y . A series of examples (some using rather sophisticated cardinal arithmetic) are given that witness that these results cannot be generalized much

The extraresolvability of some function spaces

A space X is said to be extraresolvable if X contains a family D of dense subsets such that the intersection of every two elements of D is nowhere dense and |D| > Δ(X), where Δ(X) = min{|U| : U is a nonempty open subset of X} is the dispersion character of X. In this paper, we study the extraresolvability of some function spaces Cp(X) equipped with the pointwise convergence topology. We show that Cp(X) is not extraresolvable provided that X satisfies one of the following conditions: X is metric; nw(X) = ω; X is normal; e(X) = nw(X) and either e(X) is attained or cf(e(X)) is countable. Hence, Cp(R) and Cp(Q) are not extraresolvable. We establish the equivalences 2ω ω, where [0,κ) has the order topology. We also prove that if κcf(κ) = κ and cf(κ) > ω, then Cp({0,1}κ) is extraresolvable; and that Cp(β(κ)) is extraresolvable, for every infinite cardinal κ with the discrete topology. It is shown that Cp([0,βω1)) is extraresolvable, where βω1 is the beth cardinal corresponding to ω1. Under GCH, for a compact space X, we have that cf(w(X)) > ω iff Cp(X) is extraresolvable. We proved that 2ω < 2ω1 is equivalent to the statement "Cp({0,1}ω1) is strongly extraresolvable"

Limited morbidity and possible radiographic benefit of C2

Background: The study aims to evaluate differences in alignment and clinical outcomes between surgical cervical deformity (CD) patients with a subaxial upper-most instrumented vertebra (UIV) and patients with a UIV at C2. Use of CD-corrective instrumentation in the subaxial cervical spine is considered risky due to narrow subaxial pedicles and vertebral artery anatomy. While C2 fixation provides increased stability, the literature lacks guidelines indicating extension of CD-corrective fusion from the subaxial spine to C2. Methods: Included: operative CD patients with baseline (BL) and 1-year postop (1Y) radiographic data, cervical UIV ≥ C2. Patients were grouped by UIV: C2 or subaxial (C3-C7) and propensity score matched (PSM) for BL cSVA. Mean comparison tests assessed differences in BL and 1Y patient-related, radiographic, and surgical data between UIV groups, and BL-1Y changes in alignment and clinical outcomes. Results: Following PSM, 31 C2 UIV and 31 subaxial UIV patients undergoing CD-corrective surgery were included. Groups did not differ in BL comorbidity burden (P=0.175) or cSVA (P=0.401). C2 patients were older (64 Conclusions: C2 UIV patients showed similar cervical range of motion and baseline to 1-year functional outcomes as patients with a subaxial UIV. C2 UIV patients also showed greater baseline to 1-year horizontal gaze improvement and had complication profiles similar to subaxial UIV patients, demonstrating the radiographic benefit and minimal functional loss associated with extending fusion constructs to C2. In the treatment of adult cervical deformities, extension of the reconstruction construct to the axis may allow for certain clinical benefits with less morbidity than previously acknowledged

Histone deacetylase inhibitors: potential targets responsible for their anti-cancer effect

The histone deacetylase inhibitors (HDACi) have demonstrated anticancer efficacy across a range of malignancies, most impressively in the hematological cancers. It is uncertain whether this clinical efficacy is attributable predominantly to their ability to induce apoptosis and differentiation in the cancer cell, or to their ability to prime the cell to other pro-death stimuli such as those from the immune system. HDACi-induced apoptosis occurs through altered expression of genes encoding proteins in both intrinsic and extrinsic apoptotic pathways; through effects on the proteasome/aggresome systems; through the production of reactive oxygen species, possibly by directly inducing DNA damage; and through alterations in the tumor microenvironment. In addition HDACi increase the immunogenicity of tumor cells and modulate cytokine signaling and potentially T-cell polarization in ways that may contribute the anti-cancer effect in vivo. Here, we provide an overview of current thinking on the mechanisms of HDACi activity, with attention given to the hematological malignancies as well as scientific observations arising from the clinical trials. We also focus on the immune effects of these agents

Micromechanical Properties of Injection-Molded Starch–Wood Particle Composites

The micromechanical properties of injection molded starch–wood particle composites were investigated as a function of particle content and humidity conditions. The composite materials were characterized by scanning electron microscopy and X-ray diffraction methods. The microhardness of the composites was shown to increase notably with the concentration of the wood particles. In addition,creep behavior under the indenter and temperature dependence were evaluated in terms of the independent contribution of the starch matrix and the wood microparticles to the hardness value. The influence of drying time on the density and weight uptake of the injection-molded composites was highlighted. The results revealed the role of the mechanism of water evaporation, showing that the dependence of water uptake and temperature was greater for the starch–wood composites than for the pure starch sample. Experiments performed during the drying process at 70°C indicated that the wood in the starch composites did not prevent water loss from the samples.Peer reviewe

More topological cardinal inequalities

A new topological cardinal invariant is defined; it may be considered as a weaker form of the Lindelöf degree