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We establish that a Tychonoff space X is countable if and only if C p ( X ) is strongly dominated by a second countable space. The same is true for a compact space K such that C p ( K , [ 0 , 1 ] ) is strongly dominated by a second countable space. We also prove that strong domination by a second countable space of the complement of the diagonal of a Tychonoff space X implies that X is an ℵ 0 -space. Our results solve several published open questions. [ABSTRACT FROM AUTHOR]

If C p ( X ) is jointly metrizable on compacta, then p ( X ) ≤ ω but ω 1 need not be a caliber of X . If X is either submetrizable or a P -space, then C p ( C p ( X ) ) is jointly metrizable on compacta and, in particular, all compact subsets of C p ( C p ( X ) ) are metrizable. We show that for any dyadic compact X , the space C p ( X ) is jointly metrizable on compacta. Therefore, the JCM property of C p ( X ) for a compact space X does not imply that X is separable. If X is a compact space of countable tightness and C p ( X ) is jointly metrizable on compacta, then it is independent of ZFC whether X must be separable. [ABSTRACT FROM AUTHOR]

We develop the construction of fermionic fields in terms of bosonic ones to describe free and interaction models in the circle, using thermofielddynamics. The description in the case of finite temperature is developed for both normal modes and zero modes. The treatment extends the thermofield-bosonization for periodic space. [ABSTRACT FROM AUTHOR]

We study the Bishop–Phelps–Bollobás property for numerical radius within the framework of spaces. We present several sufficient conditions on a compact space K ensuring that has the Bishop–Phelps–Bollobás property for numerical radius. In particular, we show that has such property whenever K is metrizable. [ABSTRACT FROM AUTHOR]

Let be a Fréchet space, i.e. a metrizable and complete locally convex space (lcs), its strong second dual with a defining sequence of seminorms induced by a decreasing basis of absolutely convex neighbourhoods of zero , and let be a bounded set. Let be the “worst” distance of the set of weak -cluster points in of sequences in to , and the worst distance of the weak -closure in the bidual of to , where means the natural metric of . Let , provided the involved limits exist. We extend a recent result of Angosto–Cascales to Fréchet spaces by showing that: If , there is a sequence in such that for each -cluster point of and . Moreover, iff . This provides a quantitative version of the weak angelicity in a Fréchet space. Also we show that , where is relatively compact and is the space of -valued continuous functions for a web-compact space and a separable metric space , being now the “worst” distance of the set of cluster points in of sequences in to , respect to the standard supremum metric , and . This yields a quantitative version of Orihuela’s angelic theorem. If is strongly web-compact then ; this happens if for (for instance, if is a (DF)-space or an (LF)-space). In the particular case that is a separable metrizable locally convex space then for each bounded . [ABSTRACT FROM AUTHOR]