A new type of carbon resistance thermometer with excellent thermal contact at millikelvin temperatures

Using a new brand of commercially available carbon resistor we built a cryogenic thermometer with an extremely good thermal contact to its thermal environment. Because of its superior thermal contact the thermometer is insensitive to low levels of spurious radio frequency heating. We calibrated our thermometer down to 5mK using a quartz tuning fork He-3 viscometer and measured its thermal resistance and thermal response time.Comment: 5 pages, 4 figure

Products of sequentially compact spaces and compactness with respect to a set of filters

Let $X$ be a product of topological spaces. $X$ is sequentially compact if and only if all subproducts by $\leq \mathfrak s$ factors are sequentially compact. If $\mathfrak s = \mathfrak h$, then $X$ is sequentially compact if and only if all factors are sequentially compact and all but at most $<\mathfrak s$ factors are ultraconnected. We give a topological proof of the inequality $cf \mathfrak s \geq \mathfrak h$. Recall that $\mathfrak s$ denotes the splitting number, and $\mathfrak h$ the distributivity number. Parallel results are obtained for final $\omega_n$-compactness and for other properties, as well as in the general context of a formerly introduced notion of compactness with respect to a set of filters. Some corresponding invariants are introduced.Comment: v3, entirely rewritten with many additions v4, fixed some detail