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that include the west edge, southwest corner, and south edge, and omit the southeast corner, east edge, northeast corner, north edge, and northwest corner.
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An illustration of the anti-diagonal and an open rectangle in the
Sorgenfrey plane that meets the anti-diagonal at a single point.
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are closed sets; it can be proved that they cannot be separated by open sets, showing that
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76:. The Sorgenfrey line and plane are named for the American mathematician
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Robert
Sorgenfrey, "On the topological product of paracompact spaces",
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to many otherwise plausible-sounding conjectures. It consists of the
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that is not itself a Lindelöf space. The so-called
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351:{\displaystyle \Delta \setminus K}
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87:for the Sorgenfrey plane, denoted
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139:are unions of such rectangles.
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539:. You can help Knowledge by
373:{\displaystyle \mathbb {S} }
260:{\displaystyle \mathbb {S} }
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102:{\displaystyle \mathbb {S} }
65:{\displaystyle \mathbb {R} }
482:Counterexamples in Topology
74:half-open interval topology
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386:perfectly normal spaces
477:Seebach, J. Arthur Jr.
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398:List of topologies
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271:. Note that
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403:Moore plane
233:uncountable
580:Categories
409:References
111:rectangles
72:under the
479:(1995) .
343:∖
340:Δ
312:∈
306:∣
297:−
269:subspaces
240:separable
211:∈
205:∣
196:−
178:Δ
115:Open sets
49:real line
437:(1975).
418:(1955).
392:See also
236:discrete
29:topology
509:0507446
380:is not
41:product
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382:normal
231:is an
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