Spaces in which compact subsets are closed and the lattice of T1T_1-topologies on a set

summary:We obtain some new properties of the class of KC-spaces, that is, those topological spaces in which compact sets are closed. The results are used to generalize theorems of Anderson [1] and Steiner and Steiner [12] concerning complementation in the lattice of $T_1$-topologies on a set $X$

Which topologies can have immediate successors in the lattice of T1-topologies?

[EN] We give a new characterization of those topologies which have an immediate successor or cover in the lattice of T1-topologies on a set and show that certain classes of compact and countably compact topologies do not have covers.Research supported by Consejo Nacional de Ciencia y Tecnología (México), grant 38164-E and Fundacão de Amparo a Pesquisa do Estado de São Paulo (Brasil)Alas, OT.; Wilson, RG. (2004). Which topologies can have immediate successors in the lattice of T1-topologies?. Applied General Topology. 5(2):231-242. doi:10.4995/agt.2004.1972.SWORD2312425

The Cech number of Cp(X) when X is an ordinal space

[EN] The Cech number of a space Z, C(Z), is the pseudocharacter of Z in βZ. In this article we obtain, in ZFC and assuming SCH, some upper and lower bounds of the Cech number of spaces Cp(X) of realvalued continuous functions defined on an ordinal space X with the pointwise convergence topologyResearch supported by Fapesp, CONACyT and UNAM.Alas, OT.; Tamariz-Mascarúa, Á. (2008). The Cech number of Cp(X) when X is an ordinal space. Applied General Topology. 9(1):67-76. doi:10.4995/agt.2008.1870.SWORD67769

An unfolding signifier: London's Baltic Exchange in Tallinn

In the summer of 2007 an unusual cargo arrived at Muuga and Paldiski harbors outside Tallinn. It consisted of nearly 50 containers holding over 1,000 tons of building material ranging from marble columns, staircases and fireplaces, to sculpted allegorical figures, wooden paneling and old-fashioned telephone booths. They were once part of the Baltic Exchange in the City of London. Soon they will become facets of the landscape of Tallinn. The following article charts this remarkable story and deploys this fragmented monument to analyze three issues relating to the Estonian capital: the relocation of the ‘Bronze Soldier’, the demolition of the Sakala Culture Center, and Tallinn’s future role as European Cultural Capital in 2011

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

Symptomological identification of Citrus Psorosis Virus (CPsV) in citrus orchards of Northern Cyprus

This study was conducted to perform symptomological identification of Citrus Psorosis Virus (CPsV) in Northern Cyprus. This is the oldest known citrus virus disease, which causes huge decrease in citrus fruits’ quality. The first symptoms of the disease were found in Florida and California in the 1890s. The most important and well known symptoms of CPsV are dehiscence and spalling of the trunk and branches of old trees. Chlorotic spotting and ringspot may also be caused on the leaves of infected young trees.There were reports not to kill the infected trees in the Mediterranean basin and America, but the disease leads to an important reduction in yield and fruit quality in time. Recent available verbal information among the farmers in Northern Cyprus claims that there is an increase in the symptoms of chlorotic spotting on leaves and spalling on tree trunks, which are thought to be caused by CPsV. Grafting is a common management technique on citrus trees in Northern Cyprus, where most of the varieties have been grafted on sour orange; and grafting is among the major ways of transmitting this virus, together with other mechanical practices.The results of the present study showed that the virus disease in different citrus species and varieties of Northern Cyprus are mostly symptomatic.  In the current work, citrus orchards which showed disease symptoms were all recorded and a detailed database was prepared for future molecular analyses. Thus, it is revealed that further molecular studies should be carried in order to perform a scientific investigation into the presence of this virus disease in Northern Cyprus and prove it molecularly

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"

Methodology for high-quality mobile measurement with focus on black carbon and particle mass concentrations

Measurements of air pollutants such as black carbon (BC) and particle mass concentration in general, using mobile platforms equipped with high-time-resolution instruments, have gained popularity over the last decade due to their wide range of applicability. Assuring the quality of mobile measurement, data have become more essential, particularly when the personal exposure to pollutants is related to their spatial distribution. In the following, we suggest a methodology to achieve data from mobile measurements of equivalent black carbon (eBC) and PM2:5 mass concentrations with high data quality. Besides frequent routine quality assurance measures of the instruments, the methodology includes the following steps: (a) measures to ensure the quality of mobile instruments through repeated collocated measurements using identical instrumentation, (b) inclusion of a fixed station along the route containing quality-assured reference instruments, and (c) sufficiently long and frequent intercomparisons between the mobile and reference instruments to correct the particle number and mass size distributions obtained from mobile measurements. The application of the methodology can provide the following results. First, collocated mobile measurements with sets of identical instruments allow identification of undetected malfunctions of the instruments. Second, frequent intercomparisons against the reference instruments will ensure the quality of the mobile measurement data of the eBC mass concentration. Third, the intercomparison data between the mobile optical particle size spectrometer (OPSS) and a reference mobility particle size spectrometer (MPSS) allow for the adjustment of the OPSS particle number size distribution using physically meaningful corrections. Matching the OPSS and MPSS volume particle size distributions is crucial for the determination of PM2:5 mass concentration. Using size-resolved complex refractive indices and time-resolved fine-mode volume correction factors of the fine-particle range, the calculated PM2:5 from the OPSS was within 5 % of the reference instruments (MPSSCAPSS). However, due to the nonsphericity and an unknown imaginary part of the complex refractive index of supermicrometer particles, a conversion to a volume equivalent diameter yields high uncertainties of the particle mass concentration greater than PM2:5. The proposed methodology addresses issues regarding the quality of mobile measurements, especially for health impact studies, validation of modeled spatial distribution, and development of air pollution mitigation strategies