Compact sets have important properties, and their studies have contributed to the development of functional analysis, particularly in the field of compact operators. In this paper, we introduce the ...

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Abstract: We introduce 2-compactness, a constructive function-theoretic alternative to topological compactness, based on the notions of Bishop space and Bishop morphism, which are constructive ...

The background for this paper is a dynamic programming model with a Borel state space and compact action sets. A new simple proof of the compactness of a space of measures corresponding to randomized ...

Uhlenbeck's compactness theorem can be used to analyze sequences of connections with anti-self dual curvature on principal SU(2) bundles over oriented 4-dimensional manifolds. The theorems in this ...

In this paper, we consider coupled Yang–Mills fields on vector bundle E over compact Riemannian manifold M. Under appropriate conditions on the curvature and the Higgs field, two compactness theorems ...

I will present a new compactness theorem for minimal hypersurfaces embedded in a closed Riemannian manifold N^{n+1} with n7. When n=2 and N has positive Ricci curvature, Choi and Schoen proved that a ...

The most important phenomenon in chemotaxis is cell aggregation. To model this phenomenon we use spiky or transition layer (step-function-like) steady states. In the case of one spatial dimension, we ...