Topology of the Real Numbers
... Interior and isolated points of a set belong to the set, whereas boundary and accumulation points may or may not belong to the set. In the definition of a boundary point x, we allow the possibility that x itself is a point in A belonging to (x − δ, x + δ), but in the definition of an accumulation po ...
... Interior and isolated points of a set belong to the set, whereas boundary and accumulation points may or may not belong to the set. In the definition of a boundary point x, we allow the possibility that x itself is a point in A belonging to (x − δ, x + δ), but in the definition of an accumulation po ...
DFG-Forschergruppe Regensburg/Freiburg
... be a group. An equivalence class of maps from A to B up to inner automorphisms is called a subset up to inner automorphism if it corresponds to an injective map. Grothendieck’s fundamental group is a covariant functor, denoted π1 , from the category of connected noetherian schemes to Gr. The abelian ...
... be a group. An equivalence class of maps from A to B up to inner automorphisms is called a subset up to inner automorphism if it corresponds to an injective map. Grothendieck’s fundamental group is a covariant functor, denoted π1 , from the category of connected noetherian schemes to Gr. The abelian ...
Convergence in distribution in submetric spaces
... approximation! Weak (non-metric) topologies are useful in existence problems! ...
... approximation! Weak (non-metric) topologies are useful in existence problems! ...
(A) Fuzzy Topological Spaces
... First Obstacle: A product of arbitrarily many compace fuzzy topological spaces need not be compact. Another Obstacle: Some constant functions from one fuzzy topological space to another fail to be continuous. Proposition. Let (X, δ) be a fuzzy topological space. Then every constant function from (X ...
... First Obstacle: A product of arbitrarily many compace fuzzy topological spaces need not be compact. Another Obstacle: Some constant functions from one fuzzy topological space to another fail to be continuous. Proposition. Let (X, δ) be a fuzzy topological space. Then every constant function from (X ...
INTERSECTION OF SETS WITH n
... 1. Introduction The purpose of this paper is to generalize to an arbitrary finite family of sets the following elementary fact: If in a topological space two nonempty sets, both closed or both open, have a pathwise connected union, then they have a point in common. To this end, we use the notion of ...
... 1. Introduction The purpose of this paper is to generalize to an arbitrary finite family of sets the following elementary fact: If in a topological space two nonempty sets, both closed or both open, have a pathwise connected union, then they have a point in common. To this end, we use the notion of ...
Topological constructors
... p-cells and q-cells satisfying p + q = n + 1 gives the wished (n + 1)-skeleton Zn+1 . No surprise yet. e and The possible pitfall is about topology. We must decide whether X ×Y X × Y (the product as topological spaces) are homeomorphic; not always. There e → X × Y but the inverse map is a canonical ...
... p-cells and q-cells satisfying p + q = n + 1 gives the wished (n + 1)-skeleton Zn+1 . No surprise yet. e and The possible pitfall is about topology. We must decide whether X ×Y X × Y (the product as topological spaces) are homeomorphic; not always. There e → X × Y but the inverse map is a canonical ...