Über die topologische Erweiterung von Räumen

  title={{\"U}ber die topologische Erweiterung von R{\"a}umen},
  author={A. Tychonoff},
  journal={Mathematische Annalen},
Resolvability of topological groups
A research project submitted in partial fulfilment of the requirements for the degree of Master of Science School of Mathematics, University Of Witwatersrand 18 May 2016
Cardinal functions Fθ(X) and tθ(X) for H-closed spaces
Abstract This article extends the results proved by Cammaroto and Kočinac in 1993 by showing that tθ(X) = tθ(Xs) = t(Xs) = Fθ(X) = Fθ(Xs) = F(Xs) for every H-closed and Urysohn space. Examples areExpand
Sequences and nets in topology
In a metric space, such as the real numbers with their standard metric, a set A is open if and only if no sequence with terms outside of A has a limit inside A. Moreover, a metric space is compact ifExpand
Products of Compact Spaces and the Axiom of Choice
The Tychonoff Compactness Theorem is studied for several different definitions of a compact space by researchers at the University of California, Berkeley. Expand
Monoidal topology : a categorical approach to order, metric, and topology
Preface 1. Introduction Robert Lowen and Walter Tholen 2. Monoidal structures Gavin J. Seal and Walter Tholen 3. Lax algebras Dirk Hofmann, Gavin J. Seal and Walter Tholen 4. Kleisli monoids DirkExpand
Tychonoff reflection in products and the -topology on function spaces
We show that if X is a topological space such that CR(X), the topology on X generated by the cozero sets, is not locally compact, then there is a regular space Y such that CR(X x Y) / CR(X) x CR(Y).Expand
Separation in Spaces
The ksmt calculus is a $\delta$-complete decision procedure for non-linear constraints
Property of the ksmt calculus is investigated and it is shown that it is a δ-complete decision procedure for bounded problems and an extension with local linearisations is proposed, which allow for more efficient treatment of non-linear constraints. Expand
Compactness in MV-topologies: Tychonoff theorem and Stone–Čech compactification
This paper presents a Tychonoff theorem for such a class of fuzzy topological spaces and shows an extension of the Stone–Čech compactification functor to the category of MV-topological spaces, and discusses its relationship with previous works on compactification for fuzzyTopological spaces. Expand
The Tikhonov and Alaoglu–Bourbaki Theorems
The central result of this chapter is the Alaoglu–Bourbaki theorem: Polars of neighbourhoods of zero in a locally convex space E are σ(E′, E)-compact subsets of E′. As a consequence in a dual pairExpand