LOCAL HOMEOMORPHISMS VIA ULTRAFILTER CONVERGENCE
... maps using convergence (see [7, 6, 2, 3, 4]). The recent interest on this had as starting point Janelidze-Sobral paper [6], where the authors presented characterizations of proper, perfect, open, triquotient maps and local homeomorphisms between finite topological spaces using point convergence. Thi ...
... maps using convergence (see [7, 6, 2, 3, 4]). The recent interest on this had as starting point Janelidze-Sobral paper [6], where the authors presented characterizations of proper, perfect, open, triquotient maps and local homeomorphisms between finite topological spaces using point convergence. Thi ...
Ivan Lončar
... M of a topological space X the θ-closure is defined by Clθ M = {x ∈ X: every closed neighborhood of x meets M }, M is θ-closed if Clθ M = M. This concept was used by many authors for the study of Hausdorff non-regular spaces. The θ-closure is related especially to Urysohn spaces (every pair of disti ...
... M of a topological space X the θ-closure is defined by Clθ M = {x ∈ X: every closed neighborhood of x meets M }, M is θ-closed if Clθ M = M. This concept was used by many authors for the study of Hausdorff non-regular spaces. The θ-closure is related especially to Urysohn spaces (every pair of disti ...
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 ...
Chapter 1 LOCALES AND TOPOSES AS SPACES
... than ordinary spaces. 3 The constructive reasoning makes it possible to deal with locales as though they were spaces of points. What’s more, the more stringent geometric constructivism has an intrinsic continuity – one might almost say it is the logical essence of continuity. The effect of this is t ...
... than ordinary spaces. 3 The constructive reasoning makes it possible to deal with locales as though they were spaces of points. What’s more, the more stringent geometric constructivism has an intrinsic continuity – one might almost say it is the logical essence of continuity. The effect of this is t ...
NOTES ON NON-ARCHIMEDEAN TOPOLOGICAL GROUPS
... Let G be a topological group and let w : E × F → A be a continuous biadditive mapping. A continuous birepresentation of G in w is a pair (α1 , α2 ) of continuous actions by group automorphisms α1 : G × E → E and α2 : G × F → F such that w is G-invariant, i.e., w(gx, gf ) = w(x, f ). The birepresenta ...
... Let G be a topological group and let w : E × F → A be a continuous biadditive mapping. A continuous birepresentation of G in w is a pair (α1 , α2 ) of continuous actions by group automorphisms α1 : G × E → E and α2 : G × F → F such that w is G-invariant, i.e., w(gx, gf ) = w(x, f ). The birepresenta ...
