This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in [EGH]. We prove compactness results for moduli spaces of holomorphic curves arising in Symplectic Field Theory. The theorems generalize Gromov's compactness theorem in [Gr] as well as compactness theorems in Floer homology theory, [F1, F2], and in contact geometry, [H, HWZ8].

In this paper, the new concept of near PS-compactness in L-topological spaces is introduced. It is defined for any L-subset. Its characterizations and topological properties are systematically studied. And the relationship is exposed between near PScompactness and PS-compactness, and also fuzzy compactness. 2003 Elsevier Inc. All rights reserved.

We show that the Arzelà–Ascoli theorem and Kolmogorov compactness theorem both are consequences of a simple lemma on compactness in metric spaces. Their relation to Helly’s theorem is discussed. The paper contains a detailed discussion on the historical background of the Kolmogorov compactness theorem.

This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in [EGH]. We prove compactness results for moduli spaces of holomorphic curves arising in Symplectic Field Theory. The theorems generalize Gromov's compactness theorem in [Gr] as well as compactness theorems in Floer homology theory, [F1, F2], and in contact geometry, [H, HWZ8].

This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in [EGH]. We prove compactness results for moduli spaces of holomorphic curves arising in Symplectic Field Theory. The theorems generalize Gromov’s compactness theorem in [Gr] as well as compactness theorems in Floer homology theory, [F1, F2], and in contact geometry, [H, HWZ8].

We define branch product topologies, a new product construction. Branch product topologies generalize sum topologies and product topologies. We investigate criteria for branch products or iterations of branch products to preserve various topological properties, focusing on the separation axioms and compactness. In particular, we generalize the Tychonoff Theorems for compactness and D-compactness.

In this paper, we obtain an axiomatic characterization of Lowen's fuzzy compactness. KeywordsMathematics, fuzzy sets, Topology, Lowen's compactness, operators.

The abstract model-theoretic concepts of compactness and Löwenheim–Skolem properties are investigated in the “softer” framework of pre-institutions [18]. Two compactness results are presented in this paper: a more informative reformulation of the compactness theorem for pre-institution transformations, and a theorem on natural equivalences with an abstract form of the first-order pre-institutio...

We show the relative consistency of the existence of two strongly compact cardinals κ1 and κ2 which exhibit indestructibility properties for their strong compactness, together with level by level equivalence between strong compactness and supercompactness holding at all measurable cardinals except for κ1. In the model constructed, κ1’s strong compactness is indestructible under arbitrary κ1-dir...