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...

let c be a field of subsets of a set i. also, let     1 i i be a non-decreasing positivesequence of real numbers such that 1, 1 0 1   i  and    11 i i . in this paper we prove thatbv of all the games of -bounded variation on c is a non-separable and norm dual banach space of thespace of simple games on c . we use this fact to establish the existence of a linear mapping t from...

In [8], we introduced the concept of fuzzy r-minimal structure which is an extension of smooth fuzzy topological spaces and fuzzy topological spaces in Chang's sense. And we also introduced and studied the fuzzy r-M continuity. In this paper, we introduce the concepts of fuzzy r-minimal compactness, almost fuzzy r-minimal compactness and nearly fuzzy r-minimal compactness on fuzzy r-minimal spa...

This study investigated the influence of thread pitch, helix angle, and compactness on micromotion in immediately loaded implants in bone of varying density (D2, D3, and D4). Five models of the three-dimensional finite element (0.8 mm pitch, 1.6 mm pitch, 2.4 mm pitch, double-threaded, and triple-threaded implants) in three types of bone were created using Pro/E, Hypermesh, and ABAQUS software....

We present instances of the following phenomenon: if a product of topological spaces satisfies some given compactness property then the factors satisfy a stronger compactness property, except possibly for a small number of factors. The first known result of this kind, a consequence of a theorem by A. H. Stone, asserts that if a product is regular and Lindelöf then all but at most countably many...