Coverage for local/lib/python2.7/site-packages/sage/categories/topological_spaces.py : 21%

r""" 

Topological Spaces 

""" 

#***************************************************************************** 

# Copyright (C) 2015 Travis Scrimshaw <tscrim at ucdavis.edu> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# http://www.gnu.org/licenses/ 

#****************************************************************************** 

from sage.misc.cachefunc import cached_method 

from sage.categories.category_with_axiom import CategoryWithAxiom 

from sage.categories.covariant_functorial_construction import RegressiveCovariantConstructionCategory 

from sage.categories.sets_cat import Sets 

class TopologicalSpacesCategory(RegressiveCovariantConstructionCategory): 

_functor_category = "Topological" 

def _repr_object_names(self): 

""" 

EXAMPLES:: 

sage: Groups().Topological() # indirect doctest 

Category of topological groups 

""" 

return "topological {}".format(self.base_category()._repr_object_names()) 

class TopologicalSpaces(TopologicalSpacesCategory): 

""" 

The category of topological spaces. 

EXAMPLES:: 

sage: Sets().Topological() 

Category of topological spaces 

sage: Sets().Topological().super_categories() 

[Category of sets] 

The category of topological spaces defines the topological structure, 

which shall be preserved by morphisms:: 

sage: Sets().Topological().additional_structure() 

Category of topological spaces 

TESTS:: 

sage: TestSuite(Sets().Topological()).run() 

""" 

# We must override the general object because the names don't match 

_base_category_class = (Sets,) 

def _repr_object_names(self): 

""" 

EXAMPLES:: 

sage: Sets().Topological() # indirect doctest 

Category of topological spaces 

""" 

return "topological spaces" 

class SubcategoryMethods: 

@cached_method 

def Connected(self): 

""" 

Return the full subcategory of the connected objects of ``self``. 

EXAMPLES:: 

sage: Sets().Topological().Connected() 

Category of connected topological spaces 

TESTS:: 

sage: TestSuite(Sets().Topological().Connected()).run() 

sage: Sets().Topological().Connected.__module__ 

'sage.categories.topological_spaces' 

""" 

return self._with_axiom('Connected') 

@cached_method 

def Compact(self): 

""" 

Return the subcategory of the compact objects of ``self``. 

EXAMPLES:: 

sage: Sets().Topological().Compact() 

Category of compact topological spaces 

TESTS:: 

sage: TestSuite(Sets().Topological().Compact()).run() 

sage: Sets().Topological().Compact.__module__ 

'sage.categories.topological_spaces' 

""" 

return self._with_axiom('Compact') 

class Connected(CategoryWithAxiom): 

""" 

The category of connected topological spaces. 

""" 

class Compact(CategoryWithAxiom): 

""" 

The category of compact topological spaces. 

"""