Tower extension of topological constructs

De Xue Zhang

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 1, page 41-51
  • ISSN: 0010-2628

Abstract

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Let L be a completely distributive lattice and C a topological construct; a process is given in this paper to obtain a topological construct 𝐂 ( L ) , called the tower extension of 𝐂 (indexed by L ). This process contains the constructions of probabilistic topological spaces, probabilistic pretopological spaces, probabilistic pseudotopological spaces, limit tower spaces, pretopological approach spaces and pseudotopological approach spaces, etc, as special cases. It is proved that this process has a lot of nice properties, for example, it preserves concrete reflectivity, concrete coreflectivity, and it preserves convenient hulls of topological construct, i.e., the extensional topological hulls (ETH), the cartesian closed topological hulls (CCTH) and the topological universe hulls (TUH) of topological constructs.

How to cite

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Zhang, De Xue. "Tower extension of topological constructs." Commentationes Mathematicae Universitatis Carolinae 41.1 (2000): 41-51. <http://eudml.org/doc/248610>.

@article{Zhang2000,
abstract = {Let $L$ be a completely distributive lattice and C a topological construct; a process is given in this paper to obtain a topological construct $\mathbf \{C\} (L)$, called the tower extension of $\mathbf \{C\}$ (indexed by $L$). This process contains the constructions of probabilistic topological spaces, probabilistic pretopological spaces, probabilistic pseudotopological spaces, limit tower spaces, pretopological approach spaces and pseudotopological approach spaces, etc, as special cases. It is proved that this process has a lot of nice properties, for example, it preserves concrete reflectivity, concrete coreflectivity, and it preserves convenient hulls of topological construct, i.e., the extensional topological hulls (ETH), the cartesian closed topological hulls (CCTH) and the topological universe hulls (TUH) of topological constructs.},
author = {Zhang, De Xue},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {topological construct; extensionality; cartesian closedness; tower extension; completely distributive lattice; topological category; approach space},
language = {eng},
number = {1},
pages = {41-51},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Tower extension of topological constructs},
url = {http://eudml.org/doc/248610},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Zhang, De Xue
TI - Tower extension of topological constructs
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 1
SP - 41
EP - 51
AB - Let $L$ be a completely distributive lattice and C a topological construct; a process is given in this paper to obtain a topological construct $\mathbf {C} (L)$, called the tower extension of $\mathbf {C}$ (indexed by $L$). This process contains the constructions of probabilistic topological spaces, probabilistic pretopological spaces, probabilistic pseudotopological spaces, limit tower spaces, pretopological approach spaces and pseudotopological approach spaces, etc, as special cases. It is proved that this process has a lot of nice properties, for example, it preserves concrete reflectivity, concrete coreflectivity, and it preserves convenient hulls of topological construct, i.e., the extensional topological hulls (ETH), the cartesian closed topological hulls (CCTH) and the topological universe hulls (TUH) of topological constructs.
LA - eng
KW - topological construct; extensionality; cartesian closedness; tower extension; completely distributive lattice; topological category; approach space
UR - http://eudml.org/doc/248610
ER -

References

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