A consistent counterexample in the theory of collectionwise Hausdorff spaces

1989 ◽  
Vol 65 (2) ◽  
pp. 219-224 ◽  
Author(s):  
S. Shelah
Keyword(s):  
Hausdorff Spaces ◽  
Collectionwise Hausdorff

scholarly journals Concerning collectionwise Hausdorff spaces

1974 ◽  
Vol 11 (2) ◽  
pp. 255-261
Author(s):  
James R. Boone
Keyword(s):  
Existence Theorem ◽  
Natural Setting ◽  
Hausdorff Spaces ◽  
Collectionwise Hausdorff ◽  
Moore Spaces ◽  
Convergent Sequences

In this paper the notion of a space which has property (ω) pointwise is studied. The primary application of this concept is a reformulation of Tall's existence theorem for normal non-metrizable metacompact Moore spaces in terms of families which are finite on convergent sequences. Since the first countability in Tall's theorem yields an abundance of convergent sequences, this reformulation places the existence theorem in a natural setting.

scholarly journals Compact condensations of Hausdorff spaces

2021 ◽  
Author(s):  
V. I. Belugin ◽  
A. V. Osipov ◽  
E. G. Pytkeev
Keyword(s):  
Hausdorff Spaces

scholarly journals SUBPROJECTIVITY OF PROJECTIVE TENSOR PRODUCTS OF BANACH SPACES OF CONTINUOUS FUNCTIONS

2021 ◽  
pp. 1-14
Author(s):  
R.M. CAUSEY
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Tensor Products ◽  
Continuous Functions ◽  
Hausdorff Spaces ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
Spaces Of Continuous Functions

Abstract Galego and Samuel showed that if K, L are metrizable, compact, Hausdorff spaces, then $C(K)\widehat{\otimes}_\pi C(L)$ is c0-saturated if and only if it is subprojective if and only if K and L are both scattered. We remove the hypothesis of metrizability from their result and extend it from the case of the twofold projective tensor product to the general n-fold projective tensor product to show that for any $n\in\mathbb{N}$ and compact, Hausdorff spaces K1, …, K n , $\widehat{\otimes}_{\pi, i=1}^n C(K_i)$ is c0-saturated if and only if it is subprojective if and only if each K i is scattered.

scholarly journals On modal logics arising from scattered locally compact Hausdorff spaces

2019 ◽  
Vol 170 (5) ◽  
pp. 558-577
Author(s):  
Guram Bezhanishvili ◽  
Nick Bezhanishvili ◽  
Joel Lucero-Bryan ◽  
Jan van Mill
Keyword(s):  
Modal Logics ◽  
Hausdorff Spaces ◽  
Locally Compact

scholarly journals Two semigroups of continuous relations

1977 ◽  
Vol 23 (1) ◽  
pp. 46-58 ◽  
Author(s):  
A. R. Bednarek ◽  
Eugene M. Norris
Keyword(s):  
Large Class ◽  
Algebraic Structure ◽  
Topological Spaces ◽  
Hausdorff Spaces ◽  
Completely Regular ◽  
Topological Semigroups ◽  
Stone Type

SynopsisIn this paper we define two semigroups of continuous relations on topological spaces and determine a large class of spaces for which Banach-Stone type theorems hold, i.e. spaces for which isomorphism of the semigroups implies homeomorphism of the spaces. This class includes all 0-dimensional Hausdorff spaces and all those completely regular Hausdorff spaces which contain an arc; indeed all of K. D. Magill's S*-spaces are included. Some of the algebraic structure of the semigroup of all continuous relations is elucidated and a method for producing examples of topological semigroups of relations is discussed.

scholarly journals Infinitary logic and basically disconnected compact Hausdorff spaces

2018 ◽  
Vol 28 (6) ◽  
pp. 1275-1292
Author(s):  
Antonio Di Nola ◽  
Serafina Lapenta ◽  
Ioana LeuŞtean
Keyword(s):  
Infinitary Logic ◽  
Hausdorff Spaces
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