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We demonstrate methods of constructing a Moore space in which a given metric space is densely embedded, and also investigate properties which will result in superspaces for such metric spaces which are Moore spaces with the Baire property and thereby describe properties of some spaces into which metric spaces can be densely embedded.

We demonstrate a construction that will densely embed a Moore space into a Moore space with the Baire property when this is possible. We also show how this technique generates a new ‘if and only if’ condition for determining when Moore spaces can be densely embedded in Moore spaces with the Baire property, and briefly discuss how this condition can can be used to generate new proofs that certain Moore spaces cannot be densely embedded in Moore spaces with the Baire property.

We show that, for any positive integers n and m, if a set S ⊂ Rm intersects every m − 1 dimensional affine hyperplane in Rm in exactly n points, then S is not an Fσ set. This gives a natural extension to results of Khalid Bouhjar, Jan J. Dijkstra, and R. Daniel Mauldin, who have proven this result for the case when m = 2, and also Jan J. Dijkstra and Jan van Mill, who have shown this result for the case when n = m.

This paper answers a question of Jan J. Dijkstra by giving a proof that all three-point sets are zero dimensional. It is known that all two-point sets are zero dimensional, and it is known that for all n > 3, there are n-point sets which are not zero dimensional, so this paper answers the question for the last remaining case.

‘Infinite Beauty’, an art exhibit inspired by mathematics, was held at Utah Valley University in conjunction with the university's annual Math Week, 9–13 March 2009. The art and mathematics theme o...

Understanding how climate change impacts natural systems requires investigations of the effects of environmental variation on vulnerable species and documentation of how populations respond to change. The willow beetle Chrysomela aeneicollis is ideal for such studies. It lives in California's Sierra Nevada on the southern edge of its worldwide range. Beetles experience elevated air temperatures during summertime egg laying and larval development. Exposure to these temperatures causes physiological stress, which may reduce reproductive success and endanger populations. The glycolytic enzyme phosphoglucose isomerase (PGI) is a marker of temperature adaptation in C. aeneicollis. PGI allele frequency varies across a latitudinal gradient: allele 1 is common in Rock Creek (RC), which is cooler and to the north, and allele 4 is common in Big Pine Creek (BPC), which is warmer and to the south. In populations that are intermediate in geography and climate (e.g., Bishop Creek [BC]), PGI-4 frequency increases from north to south such that alleles 1 and 4 are in relatively equal frequency in southern BC. Over the past decade, Sierra Nevada beetle populations have colonized high elevations and have become extinct at lower elevations where they were once common. In BC, the magnitude of PGI allele frequency fluctuations among life-history stages is related to maximal air temperature, with the frequency of PGI-4 increasing after the hottest part of summer. To identify mechanisms that may cause shifts in PGI allele frequency, we measured metabolic rate and fecundity for beetles collected at BC. Metabolic rate of males and females was measured at 20 degrees and 36 degrees C using flow-through respirometry. To measure laboratory fecundity, mating pairs were acclimated for 4 h each afternoon at a control temperature (20 degrees C) or at mildly elevated temperatures (26 degrees or 32 degrees C) and number of eggs laid was counted daily for 24 d, after which tissue levels of 70-kD heat shock proteins (Hsp70) were determined. Previous studies had demonstrated differences in Hsp70 expression among PGI genotypes at these temperatures. To measure field fecundity, mating pairs from BC were transplanted to similar elevations in BPC, BC, and RC and were monitored in situ for 24 d. Metabolic rate was higher for PGI 4-4 genotypes than for PGI 1-4 or PGI 1-1 individuals at 36 degrees C but not at 20 degrees C. In contrast, laboratory fecundity was greatest for females possessing PGI-1, independent of acclimation temperature. At the end of the laboratory fecundity experiment, Hsp70 expression was positively related to fecundity, suggesting minimal reproductive cost of upregulation of heat shock proteins in response to mild heat stress. In the field, fecundity was highest for PGI 1-1 and PGI 1-4 individuals in RC and PGI 4-4 individuals in BPC and was similar for all genotypes in BC. Thus, fecundity in nature was greatest for the genotypes that were most common in each area. Taken together, data reported here suggest that hot, dry summers in the Sierra Nevada may result in an increase in frequency of the PGI-4 allele and shifts to higher elevations for C. aeneicollis populations.

Background It has been consistently observed that a significant proportion of hospital inpatients are malnourished and many actually develop malnutrition in hospital. The NHS provides over 300 million meals each year at a cost of £500 million, yet there is relatively little research evaluating how well different catering systems provide for the needs of hospital inpatients. Aim The aim of the study was to: (i) evaluate whether a new steam meal catering system (Steamplicity) enables patients in theory to meet their energy requirements in hospital and (ii) compare energy and protein intake using Steamplicity with a traditional bulk cook-chill system. Methods Patients not at nutritional risk had their food intake at one lunchtime assessed. Energy intake was compared with the patients’ energy requirements and energy and protein intake were compared with previous data from a bulk system. Results Fifty-seven patients had a median daily energy requirement of 7648 kJ (1821 kcal) [inter-quartile range (IQR): 6854–9164 kJ]. Assuming 30% [2293 kJ (546 kcal)] should be supplied by the lunch meal the average intake of 1369 kJ (326 kcal) fell short by 40%. Patients served meals from Steamplicity ate less energy [1369 kJ versus 1562 kJ (326 kcal versus 372 kcal) P = 0.04] but similar protein (18 g versus 19 g P = 0.34) to the bulk system. The largest difference was the energy provided by the dessert since the bulk system served more hot high-calorie desserts. Conclusions Patient intakes did not meet their estimated requirements. The patients in this study were eating well and not at nutritional risk, thus patients with a poor appetite will be even less likely to meet their nutritional requirements. Steamplicity meals result in a lower energy intake than meals from a bulk cook-chill system, but similar protein intakes.

Summary 1. Sierra Nevada populations of the beetle Chrysomela aeneicollis experience extreme high and low temperatures during summer, which pose special challenges to larvae of limited mobility. In these populations, allele frequency variation at the glycolytic enzyme locus phosphoglucose isomerase (PGI) correlates with differences in temperature between river drainages. PGI allozymes differ in functional properties, and thermal tolerance of adults and larvae depends on PGI genotype. 2. We measured effects of temperature on larval development rate and survival after reciprocal transplantation of populations between drainages. Effects of temperature on growth rate and activity were determined after laboratory acclimation of larvae from Bishop Creek (BC), where PGI alleles 1 and 4 occur in similar frequency. Hsp70 expression levels were measured for free-living larvae of known body temperature, and for laboratory-acclimated BC larvae. 3. Larval mortality was greatest in the coldest drainage and was correlated with minimum night-time air temperature. The frequency of PGI allele 1 declined for BC larvae transplanted to the warmest drainage. Development rate of BC larvae in nature was lowest for experimental groups where PGI-1 allele frequency was highest. Larval growth and activity varied with acclimation temperature and PGI genotype in the laboratory. Hsp70 expression levels in nature were higher for larvae collected later in the day, and varied consistently among PGI genotypes in nature and in the laboratory. 4. These results suggest that daytime temperatures routinely experienced by larvae cause elevated Hsp70 expression levels indicative of physiological stress. Exposure to subzero night-time temperatures appears to cause larval mortality. Up-regulation of Hsp70 may protect larvae from heat and cold stress. Variation in Hsp70 expression among PGI genotypes may result in differential mortality and developmental rates in nature.

The leaf beetle Chrysomela aeneicollis occurs across Western North America, either at high elevation or in small, isolated populations along the coast, and thus has a highly fragmented distribution. DNA sequence data (three loci) were collected from five regions across the species range. Population connectivity was examined using traditional ecological niche modeling, which suggested that gene flow could occur among regions now and in the past. We developed geographically explicit coalescence models of sequence evolution that incorporated a two-dimensional representation of the hypothesized ranges suggested by the niche-modeling estimates. We simulated sequence data according to these models and compared them to observed sequences to identify most probable scenarios regarding the migration history of C. aeneicollis. Our results disagreed with initial niche-modeling estimates by clearly rejecting recent connectivity among regions, and were instead most consistent with a long period of range fragmentation, extending well beyond the last glacial maximum. This application of geographically explicit models of coalescence has highlighted some limitations of the use of climatic variables for predicting the present and past range of a species and has explained aspects of the Pleistocene evolutionary history of a cold-adapted organism in Western North America.

The author answers a question raised in the literature about twenty five years ago and raised again more recently in Open Problems in Topology, by G. M. Reed, concerning the conjecture that every Moore space with a σ \sigma -discrete π \pi -base can be densely embedded in a Moore space having the Baire property. Even though closely related results have made this conjecture seem likely to be true, the author shows that, surprisingly, the conjecture is false.

The problem of metrising abstract topological spaces constitutes one of the major themes of topology. Since, for each new significant class of topological spaces this question arises, the problem is always current. One of the famous metrisation problems is the Normal Moore Space Conjecture. It is known from relatively recent work that one must add special conditions in order to be able to get affirmative results for this problem. In this paper we establish such special conditions. Since these conditions are characterised by local simplicity and global coherence they are referred to in this paper generically as “abstract topological manifolds.” In particular we establish a generalisation of a classical development of Bing, giving a proof which is complete in itself, not depending on the result or arguments of Bing. In addition we show that the spaces recently developed by Collins designated as “W satisfying open G(N)” are metrisable if they are locally separable and locally connected and regular. Finally, we establish a new necessary and sufficient condition for spaces to be metrisable.

We give an affirmative answer to a question raised by Khalid Bouhjar and Jan J. Dijkstra concerning whether or not every one-dimensional partial n-point set contains an arc by showing that a partial n-point set is one-dimensional if and only if it contains an arc.

In a recent paper (5), the author has established the Euclidean spaces of least dimension in which the topological products of finite collections of k-cell-like continua can be embedded. Specifically, it was shown that, for each pair of positive integers k and n, the topological product of any collection of nk-cell-like continua can be embedded in Euclidean space of dimension k(n + 1). This result includes a theorem of Bennett (1) that the topological product of any finite collection of n snakelike continua can be embedded in Euclidean space of dimension n + 1.