Cohomology of cyro-electron microscopy
... The problem of cryo-electron microscopy (cryo-EM) asks for the following: Given a collection of noisy 2-dimensional (2D) projected images, reconstruct the 3-dimensional (3D) structure of the molecule that gave rise to these images. Viewed from a high level, it takes the form of an inverse problem si ...
... The problem of cryo-electron microscopy (cryo-EM) asks for the following: Given a collection of noisy 2-dimensional (2D) projected images, reconstruct the 3-dimensional (3D) structure of the molecule that gave rise to these images. Viewed from a high level, it takes the form of an inverse problem si ...
NEARLY COUNTABLE DENSE HOMOGENEOUS SPACES 1
... many types of countable dense sets, has in fact c many such types. We show that the question is strongly related to the Topological Vaught Conjecture. The topological sum of n copies of [0, 1) has n+1-many types of countable dense sets, while the topological sum of countably many copies of [0, 1) ha ...
... many types of countable dense sets, has in fact c many such types. We show that the question is strongly related to the Topological Vaught Conjecture. The topological sum of n copies of [0, 1) has n+1-many types of countable dense sets, while the topological sum of countably many copies of [0, 1) ha ...
Topology Proceedings
... dominated by C [12] (== X has the weak topology with respect to C in the sense of [16]), if the union of any subcollection C* of C is closed in X, and the union is determined by C*. Every space is dominated by a hereditarily closure preserving closed cover. Clearly, if X is dominated by C, then X is ...
... dominated by C [12] (== X has the weak topology with respect to C in the sense of [16]), if the union of any subcollection C* of C is closed in X, and the union is determined by C*. Every space is dominated by a hereditarily closure preserving closed cover. Clearly, if X is dominated by C, then X is ...
THE EXACT SEQUENCE OF A SHAPE FIBRATION Q. Haxhibeqiri
... to Eo = p-I (Bo) is also a shape fibration whenever Eo and Bo are P-embedded in E and B respectively (Theorem 4.1). (t"z) If e E E, b = P (e) and F = p- I (b) is P-embedded in E, then p induces an isomorphism of the homotopy pro-groups ...
... to Eo = p-I (Bo) is also a shape fibration whenever Eo and Bo are P-embedded in E and B respectively (Theorem 4.1). (t"z) If e E E, b = P (e) and F = p- I (b) is P-embedded in E, then p induces an isomorphism of the homotopy pro-groups ...
Semi-Totally Continuous Functions in Topological Spaces 1
... Proof. Suppose f : X → Y is semi-totally continuous function and A is any open set in Y . Since every open set is semi-open and f : X → Y is semi-totally continuous, it follows that f −1 (A) is clopen and hence semi-clopen in X. Thus the inverse image of each open set in Y is semi-clopen in X. There ...
... Proof. Suppose f : X → Y is semi-totally continuous function and A is any open set in Y . Since every open set is semi-open and f : X → Y is semi-totally continuous, it follows that f −1 (A) is clopen and hence semi-clopen in X. Thus the inverse image of each open set in Y is semi-clopen in X. There ...
![THE HIGHER HOMOTOPY GROUPS 1. Definitions Let I = [0,1] be](http://s1.studyres.com/store/data/001160219_1-57248e6267c8b98f385fc9eb1b30c0a7-300x300.png)
On a fuzzy topological structure
... The aim of this section is to "fuzzify" such basic set-theoretic notions as inclusion, equality, intersection and union. Here we essentially use the ideas of Z.Diskin f5]* Let X be a set and let A C X . Then A can be identified with its characteristic function. We shall use the same notation . for t ...
... The aim of this section is to "fuzzify" such basic set-theoretic notions as inclusion, equality, intersection and union. Here we essentially use the ideas of Z.Diskin f5]* Let X be a set and let A C X . Then A can be identified with its characteristic function. We shall use the same notation . for t ...
Filters in Analysis and Topology
... an ultrafilter is called free. It is worth noting that any ultrafilter which is not free is generated by a singleton, as if there exists an a with X \ {a} 6∈ F then {a} ∈ F . The complements of singletons generate the cofinite filter, so if F is not generated by a singleton then it contains the cofi ...
... an ultrafilter is called free. It is worth noting that any ultrafilter which is not free is generated by a singleton, as if there exists an a with X \ {a} 6∈ F then {a} ∈ F . The complements of singletons generate the cofinite filter, so if F is not generated by a singleton then it contains the cofi ...
General topology
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology is point-set topology.The fundamental concepts in point-set topology are continuity, compactness, and connectedness: Continuous functions, intuitively, take nearby points to nearby points. Compact sets are those that can be covered by finitely many sets of arbitrarily small size. Connected sets are sets that cannot be divided into two pieces that are far apart. The words 'nearby', 'arbitrarily small', and 'far apart' can all be made precise by using open sets, as described below. If we change the definition of 'open set', we change what continuous functions, compact sets, and connected sets are. Each choice of definition for 'open set' is called a topology. A set with a topology is called a topological space.Metric spaces are an important class of topological spaces where distances can be assigned a number called a metric. Having a metric simplifies many proofs, and many of the most common topological spaces are metric spaces.