Some articles on spaces, topological spaces, topological space, space:
Sequential Space - Categorical Properties
... The full subcategory Seq of all sequential spaces is closed under the following operations in Top Quotients Continuous closed or open images Sums Inductive limits Open and closed subspaces The ... In fact, they are the coreflective hull of metrizable spaces (i.e ... the smallest class of topological spaces closed under sums and quotients and containing the metrizable spaces) ...
... The full subcategory Seq of all sequential spaces is closed under the following operations in Top Quotients Continuous closed or open images Sums Inductive limits Open and closed subspaces The ... In fact, they are the coreflective hull of metrizable spaces (i.e ... the smallest class of topological spaces closed under sums and quotients and containing the metrizable spaces) ...
Hing Tong - Important Publications
... Hing Tong, "On Ideals Associated with Certain Normed Rings over Topological Spaces", Columbia University, Ph.D ... of Certain Topologized Rings of Continuous Mappings Associated with Topological Spaces", The Annals of Mathematics, 2nd Series, Vol ... of normal and perfectly normal spaces", Duke Math ...
... Hing Tong, "On Ideals Associated with Certain Normed Rings over Topological Spaces", Columbia University, Ph.D ... of Certain Topologized Rings of Continuous Mappings Associated with Topological Spaces", The Annals of Mathematics, 2nd Series, Vol ... of normal and perfectly normal spaces", Duke Math ...
Adjoint Functors - Examples - Further Examples - Topology
... Let G be the functor from topological spaces to sets that associates to every topological space its underlying set (forgetting the topology, that is) ... G has a left adjoint F, creating the discrete space on a set Y, and a right adjoint H creating the trivial topology on Y ... Suspensions and loop spaces Given topological spaces X and Y, the space of homotopy classes of maps from the suspension SX of X to Y is naturally isomorphic to the space of homotopy classes of maps from X to the loop ...
... Let G be the functor from topological spaces to sets that associates to every topological space its underlying set (forgetting the topology, that is) ... G has a left adjoint F, creating the discrete space on a set Y, and a right adjoint H creating the trivial topology on Y ... Suspensions and loop spaces Given topological spaces X and Y, the space of homotopy classes of maps from the suspension SX of X to Y is naturally isomorphic to the space of homotopy classes of maps from X to the loop ...
Tube Lemma
... Before giving the lemma, one notes the following terminology If X and Y are topological spaces and X × Y is the product space, a slice in X × Y is ... Using the concept of closed maps, this can be rephrased concisely as follows if X is any topological space and Y a compact space, then the projection map X × Y ... Generalized Tube Lemma Let X and Y be topological spaces and consider the product space X × Y ...
... Before giving the lemma, one notes the following terminology If X and Y are topological spaces and X × Y is the product space, a slice in X × Y is ... Using the concept of closed maps, this can be rephrased concisely as follows if X is any topological space and Y a compact space, then the projection map X × Y ... Generalized Tube Lemma Let X and Y be topological spaces and consider the product space X × Y ...
Delta Set - Related Functors
... above defines a covariant functor from the category of Δ-sets to the category of topological spaces ... Geometric realization takes a Δ-set to a topological space, and carries maps of Δ-sets to induced continuous maps between geometric realizations (which are ... Given any topological space X, one can construct a Δ-set as follows ...
... above defines a covariant functor from the category of Δ-sets to the category of topological spaces ... Geometric realization takes a Δ-set to a topological space, and carries maps of Δ-sets to induced continuous maps between geometric realizations (which are ... Given any topological space X, one can construct a Δ-set as follows ...
Famous quotes containing the word spaces:
“Though there were numerous vessels at this great distance in the horizon on every side, yet the vast spaces between them, like the spaces between the stars,—far as they were distant from us, so were they from one another,—nay, some were twice as far from each other as from us,—impressed us with a sense of the immensity of the ocean, the “unfruitful ocean,” as it has been called, and we could see what proportion man and his works bear to the globe.”
—Henry David Thoreau (1817–1862)
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