# A note on coclones of topological spaces

Commentationes Mathematicae Universitatis Carolinae (2011)

- Volume: 52, Issue: 3, page 403-416
- ISSN: 0010-2628

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topBarkhudaryan, Artur. "A note on coclones of topological spaces." Commentationes Mathematicae Universitatis Carolinae 52.3 (2011): 403-416. <http://eudml.org/doc/246483>.

@article{Barkhudaryan2011,

abstract = {The clone of a topological space is known to have a strictly more expressive first-order language than that of the monoid of continuous self-maps. The current paper studies coclones of topological spaces (i.e. clones in the category dual to that of topological spaces and continuous maps) and proves that, in contrast to clones, the first-order properties of coclones cannot express anything more than those of the monoid, except for the case of discrete and indiscrete spaces.},

author = {Barkhudaryan, Artur},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {clone; coclone; monoid of continuous self-maps; clone theory; monoid theory; clone; coclone; monoid of continuous self-maps; clone theory; monoid theory},

language = {eng},

number = {3},

pages = {403-416},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {A note on coclones of topological spaces},

url = {http://eudml.org/doc/246483},

volume = {52},

year = {2011},

}

TY - JOUR

AU - Barkhudaryan, Artur

TI - A note on coclones of topological spaces

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2011

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 52

IS - 3

SP - 403

EP - 416

AB - The clone of a topological space is known to have a strictly more expressive first-order language than that of the monoid of continuous self-maps. The current paper studies coclones of topological spaces (i.e. clones in the category dual to that of topological spaces and continuous maps) and proves that, in contrast to clones, the first-order properties of coclones cannot express anything more than those of the monoid, except for the case of discrete and indiscrete spaces.

LA - eng

KW - clone; coclone; monoid of continuous self-maps; clone theory; monoid theory; clone; coclone; monoid of continuous self-maps; clone theory; monoid theory

UR - http://eudml.org/doc/246483

ER -

## References

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