Various Topologies Generated from <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-7.2982pt" id="M1" height="18.6976pt" version="1.1" viewBox="-0.0657574 -11.3994 16.4976 18.6976" width="16.4976pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-70" d="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z"/></g><g transform="matrix(.012,0,0,-0.012,10.485,4.134)"><path id="g50-107" d="M400 606C400 634 383 656 353 656C316 656 294 620 294 593C294 564 317 545 343 545C375 545 400 573 400 606ZM366 351C379 413 381 451 356 451C323 451 251 408 183 341L199 313C223 335 267 365 277 365C285 365 284 354 277 312C245 132 222 27 193 -100C182 -148 160 -188 131 -188C113 -188 90 -178 75 -170C64 -164 55 -168 48 -175C38 -185 24 -203 24 -222S48 -257 71 -257C89 -257 131 -241 186 -192C243 -141 286 -46 310 74L366 351Z"/></g></svg>-</span>Neighbourhoods via Ideals

<div>The <svg height="12.0653pt" id="M998" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -8.6359 5.61923 12.0653" width="5.61923pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M394 607C394 634 378 655 350 655C315 655 294 620 294 594C294 564 314 546 339 546C372 546 394 574 394 607ZM360 349C373 414 374 448 351 448C321 448 249 404 183 338L197 313C223 336 265 367 276 367C285 367 283 355 275 313C241 129 220 23 189 -102C175 -158 153 -197 124 -197C106 -197 85 -187 70 -177C64 -173 51 -177 44 -183C34 -193 23 -209 23 -228C23 -244 46 -261 67 -261C86 -261 127 -245 181 -197C237 -147 279 -52 303 66L360 349Z"></path></g></svg> approximations for each <span class="nowrap"><svg height="12.7178pt" id="M999" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 147.22 12.7178" width="147.22pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g 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Complexity

tab5

Table 5

Table 5: Various Topologies Generated from <span class="nowrap"><svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-7.2982pt" id="M1" height="18.6976pt" version="1.1" viewBox="-0.0657574 -11.3994 16.4976 18.6976" width="16.4976pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-70" d="M593 650H142L136 622C219 616 224 611 209 531L130 120C114 39 108 34 23 28L17 0H501C518 32 557 130 568 158L540 169C519 132 495 93 469 70C439 43 409 35 332 35C272 35 241 37 225 50C211 61 211 89 222 149L253 320H350C441 320 443 312 441 239H471L510 434H481C455 366 448 358 360 358H260L303 572C311 613 312 615 348 615H431C509 615 522 603 532 581C544 555 546 531 545 491L574 493C583 555 592 631 593 650Z"/></g><g transform="matrix(.012,0,0,-0.012,10.485,4.134)"><path id="g50-107" d="M400 606C400 634 383 656 353 656C316 656 294 620 294 593C294 564 317 545 343 545C375 545 400 573 400 606ZM366 351C379 413 381 451 356 451C323 451 251 408 183 341L199 313C223 335 267 365 277 365C285 365 284 354 277 312C245 132 222 27 193 -100C182 -148 160 -188 131 -188C113 -188 90 -178 75 -170C64 -164 55 -168 48 -175C38 -185 24 -203 24 -222S48 -257 71 -257C89 -257 131 -241 186 -192C243 -141 286 -46 310 74L366 351Z"/></g></svg>-</span>Neighbourhoods via Ideals 

Complexity

Various Topologies Generated from -Neighbourhoods via Ideals

Table 5