| 词条 | Toronto space |
| 释义 |
In mathematics, in the realm of point-set topology, a Toronto space is a topological space that is homeomorphic to every proper subspace of the same cardinality. There are five homeomorphism classes of countable Toronto spaces, namely: the discrete topology, the indiscrete topology, the cofinite topology and the upper and lower topologies on the natural numbers. The only countable Hausdorff Toronto space is the discrete space.[1] The Toronto space problem asks for an uncountable Toronto Hausdorff space that is not discrete.[2] References1. ^{{citation | last = Bonnet | first = Robert | contribution = On superatomic Boolean algebras | location = Dordrecht | mr = 1261195 | pages = 31–62 | publisher = Kluwer Acad. Publ. | series = NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. | title = Finite and infinite combinatorics in sets and logic (Banff, AB, 1991) | volume = 411 | year = 1993}}. {{topology-stub}}2. ^{{citation|title=Open problems in topology, Volume 1|first1=J.|last1=van Mill|first2=George M.|last2=Reed|page=15|publisher=North-Holland|year=1990|isbn=9780444887689}}. 2 : Properties of topological spaces|Homeomorphisms |
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